Classes of words τ of size 4,5 according to pattern τ avoiding compositions with parts in N={1,2,3,...}.
Let [k]m be the set of all words π=π1π2…πm on the alphabet {1,2,...,k} of length m. A composition of n with parts in N={1,2,...} is a word π=π1π2…πm of length m such that π1+π2+…+πm=n. We say k-ary word π=π1π2…πnof length n contains a k'-ary word τ of length n' if there exists a subsequence 1≤i1<…<in'≤n such that πi1πi2…πin' is order-isomorphic to τ. Otherwise, we say π avoids τ. We denote the set of all compositions of n with parts in N that avoid τ by Cn(τ). Two words τ and τ' are equivalent if there is a size-preserving bijection between the sets Cn(τ) and Cn(τ').
Patterns of size 4:
- |Cn(1112)|n=0...24=|Cn(1121)|n=0...24
=1,1,2,4,8,15,29,54,101,185,335,597 ,1067,1872,3257,5626 ,9655 ,16374,27655 ,46240 ,77075 ,127434,209453 ,341764 ,555698.
- |Cn(1111)|n=0...24
=1,1,2,4,7,15,26,52, 93,173,310,556 ,1041,1789,3098,5620 ,9725 ,16377,28764 ,48518 ,82889 ,137161,237502 ,390084 ,646347.
- |Cn(2112)|n=0...24
=1,1,2,4,8,16,31,61,118,228,433,819 ,1536,2858,5283,9679 ,17621,31811,57081 ,101691,180111,316951,554561 ,964485 ,1668026.
- |Cn(1212)|n=0...24
=1,1,2,4,8,16,31,61,118,228,433,819 ,1535,2857,5280,9675 ,17609,31791,57043 ,101638,180057,316955,554777 ,965283 ,1670341.
- |Cn(1221)|n=0...24
=1,1,2,4,8,16,31,61,118,228,433,819 ,1536,2860,5289,9695 ,17659,31909,57319 ,102253,181381,319715,560407 ,976597 ,1692732.
- |Cn(1122)|n=0...24
=1,1,2,4,8,16,31,61,118,228,433,819 ,1538,2866,5303,9729 ,17741,32105,57767 ,103235,183465,324009,569113 ,993995 ,1726932.
- |Cn(1312)|n=0...24
=1,1,2,4,8,16,32,63,124,241,466,892 ,1694,3191,5962,11054,20340,37161,67418 ,121524,217661,387562,686136 ,1208267,2116810.
- |Cn(1231)|n=0...24
=1,1,2,4,8,16,32,63,124,241,466,892 ,1694,3192,5967,11072,20395,37315,67813 ,122485,219897,392573,697020 ,1231297,2164445.
- |Cn(2113)|n=0...24
=1,1,2,4,8,16,32,63,124,241,466,892 ,1694,3193,5970,11081,20420,37378,67960 ,122823,220639,394149,700295 ,1237957,2177740.
- |Cn(1213)|n=0...24
=1,1,2,4,8,16,32,63,124,241,466,892 ,1694,3193,5970,11082,20424,37392,68004 ,122946,220961,394948,702193 ,1242302,2187393.
- |Cn(1123)|n=0...24=|Cn(1132)|n=0...24
=1,1,2,4,8,16,32,63,124,241,466,892 ,1694,3193,5971,11086,20436,37427,68096 ,123170,221485,396128,704754 ,1247712,2198554.
- |Cn(1222)|n=0...24=|Cn(2122)|n=0...24
=1,1,2,4,8,16,32,63,124,244,477,927 ,1793,3451,6607,12578,23824,44909,84261 ,157331,292357,540667,995338 ,1824181,3328584.
- |Cn(1223)|n=0...24=|Cn(1232)|n=0...24=|Cn(1322)|n=0...24=|Cn(2123)|n=0...24=|Cn(2132)|n=0...24=|Cn(2213)|n=0...24
=1,1,2,4,8,16,32,64,127,251,494,967 ,1882,3642,7006,13401,25490,48219,90722 ,169789,316127,585660,1079755,1981407,3619549.
- |Cn(2313)|n=0...24
=1,1,2,4,8,16,32,64,128,255,508,1009,2001,3957,7808,15364,30154,59019,115202,224253,435348,842864,1627482,3134190,6020078.
- |Cn(1332)|n=0...24
=1,1,2,4,8,16,32,64,128,255,508,1009,2001,3957,7808,15364,30154,59021,115210,224285,435447,843157,1628279,3136275,6025299.
- |Cn(1323)|n=0...24
=1,1,2,4,8,16,32,64,128,255,508,1009,2001,3957,7808,15364,30154,59021,115210,224285,435449,843165,1628312,3136381,6025619.
- |Cn(3123)|n=0...24
=1,1,2,4,8,16,32,64,128,255,508,1009,2001,3957,7808,15364,30155,59024,115222,224319,435546,843417,1628950,3137925,6029274.
- |Cn(1233)|n=0...24=|Cn(2133)|n=0...24
=1,1,2,4,8,16,32,64,128,255,508,1009,2001,3957,7808,15364,30155,59025,115226,224334,435591,843544,1629284,3138770,6031329.
- |Cn(2413)|n=0...24
=1,1,2,4,8,16,32,64,128,256,511,1019,2028,4028,7981,15777,31108,61181,120014,234818,458273,892134,1732500,3356468,6487681.
- |Cn(1423)|n=0...24
=1,1,2,4,8,16,32,64,128,256,511,1019,2028,4028,7981,15777,31108,61181,120014,234819,458278,892154,1732568,3356678,6488279.
- |Cn(1342)|n=0...24
=1,1,2,4,8,16,32,64,128,256,511,1019,2028,4028,7981,15777,31108,61181,120014,234819,458278,892156,1732578,3356721,6488429.
- |Cn(2314)|n=0...24
=1,1,2,4,8,16,32,64,128,256,511,1019,2028,4028,7981,15777,31108,61182,120019,234839,458346,892365,1733176,3358335,6492597.
- |Cn(3124)|n=0...24
=1,1,2,4,8,16,32,64,128,256,511,1019,2028,4028,7981,15777,31108,61182,120019,234839,458346,892366,1733182,3358362,6492696.
- |Cn(1234)|n=0...24=|Cn(1243)|n=0...24=|Cn(1432)|n=0...24=|Cn(2134)|n=0...24=|Cn(2143)|n=0...24=|Cn(3214)|n=0...24
=1,1,2,4,8,16,32,64,128,256,511,1019,2028,4028,7981,15777,31108,61182,120019,234840,458351,892386,1733249,3358567,6493277.
- |Cn(1324)|n=0...24
=1,1,2,4,8,16,32,64,128,256,511,1019,2028,4028,7981,15777,31108,61182,120019,234840,458351,892387,1733255,3358594,6493377.
Patterns of size 5:
| Pattern τ |
|C20(τ)| |
|C21(τ)| |
|C22(τ)| |
|C23(τ)| |
|C24(τ)| |
|C25(τ)| |
|C26(τ)| |
|C27(τ)| |
|C28(τ)| |
|C29(τ)| |
|C30(τ)| |
|C31(τ)| |
|C32(τ)| |
| 11112,11121,11211 | 170944 | 299744 | 522829 | 905728 | 1561794 |
| 11111 | 170015 | 303356 | 536877 | 932679 | 1637383 |
| 12112 | 277374 | 506651 | 920031 | 1661532 | 2984319 |
| 21112 | 277480 | 506816 | 920330 | 1661916 | 2984760 |
| 11212 | 278222 | 508621 | 924526 | 1671457 | 3005810 |
| 12121 | 278276 | 508768 | 924892 | 1672346 | 3007872 |
| 11221 | 280120 | 512922 | 933962 | 1691750 | 3048552 |
| 11122 | 280794 | 514454 | 937414 | 1699250 | 3064692 |
| 13112 | 317119 | 585160 | 1073587 | 1958783 | 3554467 |
| 11312 | 317346 | 585816 | 1075372 | 1963346 | 3565653 |
| 12131 | 317628 | 586559 | 1077226 | 1967786 | 3575872 |
| 11231 | 318174 | 587969 | 1080694 | 1975987 | 3594640 |
| 21113 | 318202 | 588047 | 1080918 | 1976550 | 3595962 |
| 11321 | 318264 | 588201 | 1081275 | 1977378 | 3597877 |
| 12113 | 318265 | 588243 | 1081479 | 1978055 | 3599799 |
| 11213 | 318412 | 588642 | 1082499 | 1980553 | 3605700 |
| 11123,11132 | 318804 | 589632 | 1084872 | 1986054 | 3618082 |
| 21212 | 369350 | 698204 | 1314047 | 2462440 | 4594680 |
| 12122 | 369389 | 698312 | 1314338 | 2463181 | 4596534 |
| 12212 | 369381 | 698303 | 1314327 | 2463196 | 4596646 |
| 12221 | 369544 | 698720 | 1315359 | 2465690 | 4602480 |
| 21122 | 369782 | 699234 | 1316421 | 2467784 | 4606410 |
| 11222 | 370136 | 700162 | 1318781 | 2473590 | 4620294 |
| 21312 | 392795 | 744739 | 1405410 | 2639921 | 4936338 |
| 13212 | 392822 | 744825 | 1405658 | 2640589 | 4938041 |
| 13122 | 393012 | 745249 | 1406555 | 2642401 | 4941526 |
| 21132 | 392964 | 745170 | 1406468 | 2642420 | 4942050 |
| 12312 | 392999 | 745302 | 1406880 | 2643593 | 4945188 |
| 21213 | 393008 | 745334 | 1406977 | 2643861 | 4945872 |
| 12132 | 393010 | 745344 | 1407015 | 2643987 | 4946251 | 9212699 |
| 12123 | 393010 | 745344 | 1407015 | 2643987 | 4946251 | 9212703 |
| 21123 | 393055 | 745435 | 1407185 | 2644256 | 4946564 |
| 12231 | 393092 | 745510 | 1407324 | 2644500 | 4946943 |
| 12213 | 393154 | 745715 | 1407936 | 2646195 | 4951406 |
| 12321 | 393159 | 745731 | 1407980 | 2646307 | 4951672 |
| 22113 | 393413 | 746377 | 1409556 | 2650021 | 4960144 |
| 11223,11232,11322 | 393429 | 746443 | 1409778 | 2650699 | 4962054 |
| 12222,21222,22122 | 428952 | 827634 | 1591632 | 3050965 | 5829342 |
| 12223,12232,12322 |
| 13222,21223,21232 | 445647 | 861514 | 1659551 | 3185466 | 6092743 |
| 21322,22123,22132,22213 |
| 13132 | 472809 | 924977 | 1805122 | 3514011 | 6823654 |
| 21313 | 472818 | 925013 | 1805231 | 3514337 | 6824536 |
| 12313 | 472823 | 925037 | 1805331 | 3514671 | 6825565 |
| 13123 | 472823 | 925038 | 1805341 | 3514713 | 6825727 |
| 13213 | 472825 | 925047 | 1805376 | 3514829 | 6826077 |
| 13231 | 472847 | 925107 | 1805539 | 3515235 | 6827061 |
| 13312 | 472854 | 925129 | 1805596 | 3515373 | 6827360 |
| 12331 | 472857 | 925146 | 1805668 | 3515622 | 6828139 |
| 23113 | 472903 | 925247 | 1805875 | 3515993 | 6828696 |
| 31123 | 472918 | 925309 | 1806086 | 3516651 | 6830599 |
| 31213 | 472929 | 925355 | 1806229 | 3517085 | 6831797 |
| 11332 | 472947 | 925405 | 1806383 | 3517501 | 6832927 |
| 11323 | 472947 | 925405 | 1806382 | 3517506 | 6832945 |
| 21133 | 472963 | 925467 | 1806569 | 3518047 | 6834381 |
| 12133 | 472963 | 925467 | 1806574 | 3518069 | 6834471 |
| 11233 | 472963 | 925471 | 1806593 | 3518139 | 6834703 |
| 13142 | 488636 | 960244 | 1882770 | 3683216 | 7189065 |
| 14213 | 488638 | 960253 | 1882806 | 3683339 | 7189448 |
| 21413 | 488638 | 960254 | 1882810 | 3683354 | 7189492 |
| 12413 | 488638 | 960255 | 1882816 | 3683383 | 7189608 |
| 13412 | 488639 | 960260 | 1882839 | 3683461 | 7189854 |
| 14123 | 488643 | 960272 | 1882872 | 3683543 | 7190038 |
| 14312 | 488640 | 960265 | 1882861 | 3683542 | 7190126 |
| 21314 | 488640 | 960267 | 1882874 | 3683602 | 7190350 |
| 12431 | 488644 | 960278 | 1882898 | 3683640 | 7190366 |
| 13124 | 488640 | 960267 | 1882874 | 3683604 | 7190369 |
| 13241 | 488644 | 960279 | 1882902 | 3683653 | 7190403 |
| 14132 | 488645 | 960283 | 1882916 | 3683698 | 7190536 |
| 24113 | 488674 | 960372 | 1883160 | 3684321 | 7192033 |
| 12314 | 488665 | 960355 | 1883152 | 3684414 | 7192588 |
| 13214 | 488665 | 960355 | 1883154 | 3684425 | 7192639 |
| 12341 | 488666 | 960358 | 1883161 | 3684437 | 7192641 |
| 31124 | 488679 | 960398 | 1883271 | 3684719 | 7193333 |
| 11423 | 488682 | 960408 | 1883297 | 3684785 | 7193473 |
| 11342 | 488682 | 960408 | 1883297 | 3684784 | 7193477 |
| 31214 | 488680 | 960405 | 1883302 | 3684837 | 7193723 |
| 21134,21143 | 488680 | 960405 | 1883304 | 3684847 | 7193765 |
| 12134,12143 | 488681 | 960410 | 1883324 | 3684917 | 7193987 |
| 23114 | 488685 | 960422 | 1883355 | 3684984 | 7194103 |
| 32114 | 488685 | 960422 | 1883358 | 3685000 | 7194171 |
| 11234,11243,11432 | 488686 | 960428 | 1883383 | 3685094 | 7194484 |
| 11324 | 488686 | 960428 | 1883383 | 3685094 | 7194488 |
| 23213 | 494582 | 974957 | 1918100 | 3765918 | 7378434 |
| 23132 | 494584 | 974968 | 1918147 | 3766082 | 7378953 |
| 23123 | 494587 | 974977 | 1918166 | 3766118 | 7378999 |
| 12323 | 494587 | 974979 | 1918177 | 3766166 | 7379166 | 14427727 | 28148807 | 54800750 | 106456739 | 206356820 |
| 21323 | 494587 | 974979 | 1918177 | 3766166 | 7379166 | 14427727 | 28148807 | 54800750 | 106456739 | 206356816 |
| 13232 | 494587 | 974979 | 1918177 | 3766166 | 7379168 |
| 31223 | 494594 | 975010 | 1918282 | 3766474 | 7379986 |
| 13223 | 494594 | 975009 | 1918280 | 3766474 | 7380013 |
| 32123 | 494594 | 975010 | 1918289 | 3766518 | 7380183 |
| 21332 | 494594 | 975012 | 1918300 | 3766567 | 7380361 |
| 12332 | 494594 | 975012 | 1918302 | 3766581 | 7380425 |
| 22313 | 494598 | 975033 | 1918388 | 3766862 | 7381265 |
| 13322 | 494608 | 975078 | 1918547 | 3767380 | 7382805 |
| 12233,21233,22133 | 494608 | 975080 | 1918559 | 3767434 | 7382995 |
| 24213 | 504899 | 998671 | 1971813 | 3886039 | 7644090 |
| 24123 | 504899 | 998671 | 1971813 | 3886039 | 7644095 |
| 13242 | 504899 | 998671 | 1971813 | 3886042 | 7644116 | 15007564 | 29406726 | 57508444 |
| 12423 | 504899 | 998671 | 1971813 | 3886042 | 7644116 | 15007566 | 29406736 | 57508486 | 112244393 | 218649086 | 425095725 | 824879229 |
| 21423 | 504899 | 998671 | 1971813 | 3886042 | 7644116 | 15007566 | 29406736 | 57508486 | 112244393 | 218649086 | 425095725 | 824879228 |
| 21342 | 504899 | 998673 | 1971830 | 3886132 | 7644491 |
| 23142 | 504900 | 998679 | 1971856 | 3886222 | 7644769 |
| 12342 | 504900 | 998680 | 1971862 | 3886250 | 7644877 |
| 21432 | 504900 | 998680 | 1971864 | 3886263 | 7644938 |
| 12432 | 504900 | 998680 | 1971864 | 3886263 | 7644939 |
| 14223 | 504901 | 998687 | 1971893 | 3886361 | 7645226 |
| 22413 | 504901 | 998687 | 1971895 | 3886375 | 7645294 |
| 14232 | 504901 | 998687 | 1971895 | 3886375 | 7645298 |
| 31224 | 504901 | 998687 | 1971897 | 3886387 | 7645347 |
| 32214 | 504901 | 998687 | 1971897 | 3886387 | 7645350 |
| 32124 | 504901 | 998687 | 1971897 | 3886387 | 7645352 |
| 23124 | 504901 | 998687 | 1971897 | 3886387 | 7645353 | 15011590 |
| 23214 | 504901 | 998687 | 1971897 | 3886387 | 7645353 | 15011589 |
| 13224 | 504901 | 998687 | 1971897 | 3886388 | 7645357 |
| 12324 | 504901 | 998687 | 1971897 | 3886389 | 7645366 | 15011651 | 29419180 | 57544352 | 112343292 | 218911964 | 425773182 | 826579262 |
| 21324 | 504901 | 998687 | 1971897 | 3886389 | 7645366 | 15011651 | 29419180 | 57544352 | 112343292 | 218911964 | 425773182 | 826579261 |
| 13422 | 504901 | 998688 | 1971901 | 3886403 | 7645401 |
| 22314 | 504901 | 998687 | 1971899 | 3886402 | 7645425 |
| 14322 | 504901 | 998688 | 1971904 | 3886424 | 7645504 |
| 12234,12243,21234 |
| 21243,22134,22143 | 504901 | 998688 | 1971905 | 3886430 | 7645532 |
| 23313 | 511953 | 1017130 | 2018679 | 4002039 | 7924995 |
| 23133 | 511953 | 1017130 | 2018679 | 4002039 | 7924996 |
| 31323 | 511953 | 1017130 | 2018679 | 4002039 | 7924998 |
| 13323 | 511953 | 1017130 | 2018679 | 4002039 | 7925003 | 15674892 | 30965800 |
| 13332 | 511953 | 1017130 | 2018679 | 4002039 | 7925003 | 15674892 | 30965797 |
| 13233 | 511953 | 1017130 | 2018679 | 4002039 | 7925004 |
| 31233 | 511954 | 1017135 | 2018700 | 4002114 | 7925241 |
| 32133 | 511954 | 1017135 | 2018700 | 4002114 | 7925242 |
| 12333,21333 | 511954 | 1017135 | 2018700 | 4002114 | 7925246 |
| 24313 | 516589 | 1027944 | 2043430 | 4057772 | 8048745 |
| 23413 | 516589 | 1027944 | 2043430 | 4057772 | 8048750 | 15946331 |
| 31324 | 516589 | 1027944 | 2043430 | 4057772 | 8048750 | 15946334 | 31554879 |
| 23134 | 516589 | 1027944 | 2043430 | 4057772 | 8048750 | 15946334 | 31554899 | 62363616 | 123095495 | 242655378 | 477713441 | 939225481 | 1844141265 |
| 23143 | 516589 | 1027944 | 2043430 | 4057772 | 8048750 | 15946334 | 31554899 | 62363616 | 123095495 | 242655378 | 477713441 | 939225481 | 1844141264 |
| 31423 | 516589 | 1027944 | 2043431 | 4057777 | 8048767 |
| 24133 | 516589 | 1027944 | 2043432 | 4057784 | 8048801 | 15946514 | 31555463 |
| 13342 | 516589 | 1027944 | 2043432 | 4057784 | 8048801 | 15946514 | 31555465 |
| 14233 | 516589 | 1027944 | 2043432 | 4057784 | 8048801 | 15946514 | 31555467 |
| 13423 | 516589 | 1027944 | 2043432 | 4057784 | 8048804 | 15946534 | 31555563 | 62365649 | 123101367 | 242671568 |
| 13432 | 516589 | 1027944 | 2043432 | 4057784 | 8048804 | 15946534 | 31555563 | 62365649 | 123101367 | 242671567 | 477720039 |
| 14332 | 516589 | 1027944 | 2043432 | 4057784 | 8048804 | 15946534 | 31555563 | 62365649 | 123101367 | 242671567 | 477756437 |
| 23314 | 516589 | 1027944 | 2043432 | 4057784 | 8048804 | 15946535 | 31555566 |
| 14323 | 516589 | 1027944 | 2043432 | 4057784 | 8048804 | 15946535 | 31555569 |
| 13324 | 516589 | 1027944 | 2043432 | 4057784 | 8048804 | 15946535 | 31555570 |
| 32314 | 516589 | 1027944 | 2043432 | 4057784 | 8048804 | 15946535 | 31555580 |
| 13234 | 516589 | 1027944 | 2043432 | 4057784 | 8048804 | 15946535 | 31555582 | 62365740 | 123101723 | 242672811 | 477760435 | 939348262 | 1844453674 |
| 13243 | 516589 | 1027944 | 2043432 | 4057784 | 8048804 | 15946535 | 31555582 | 62365740 | 123101723 | 242672811 | 477760435 | 939348262 | 1844453673 |
| 31243 | 516589 | 1027945 | 2043436 | 4057798 | 8048843 |
| 32143 | 516589 | 1027945 | 2043437 | 4057804 | 8048869 |
| 31234 | 516589 | 1027945 | 2043437 | 4057805 | 8048877 | 15946767 | 31556254 |
| 32134 | 516589 | 1027945 | 2043437 | 4057805 | 8048877 | 15946767 | 31556256 |
| 33124 | 516589 | 1027945 | 2043438 | 4057811 | 8048903 | 15946861 | 31556255 |
| 33214 | 516589 | 1027945 | 2043438 | 4057811 | 8048903 | 15946861 | 31556258 |
| 12334,12343,12433 |
| 21334,21343,21433 | 516589 | 1027945 | 2043438 | 4057811 | 8048903 | 15946861 | 31556259 |
| 14243 | 522145 | 1042632 | 2081196 | 4152622 | 8282198 | 16510861 | 32899031 |
| 13424 | 522145 | 1042632 | 2081196 | 4152622 | 8282198 | 16510863 | 32899043 | 65520227 |
| 31424 | 522145 | 1042632 | 2081196 | 4152622 | 8282198 | 16510863 | 32899043 | 65520226 |
| 24143 | 522145 | 1042632 | 2081196 | 4152622 | 8282198 | 16510865 | 32899053 |
| 24134 | 522145 | 1042632 | 2081196 | 4152622 | 8282198 | 16510867 | 32899066 |
| 24314 | 522145 | 1042632 | 2081196 | 4152622 | 8282198 | 16510867 | 32899067 |
| 14342 | 522145 | 1042632 | 2081196 | 4152622 | 8282200 | 16510875 | 32899100 |
| 13442 | 522145 | 1042632 | 2081196 | 4152622 | 8282200 | 16510877 | 32899111 | 65520497 |
| 24413 | 522145 | 1042632 | 2081196 | 4152622 | 8282200 | 16510877 | 32899111 | 65520496 |
| 32414 | 522145 | 1042632 | 2081196 | 4152623 | 8282205 | 16510899 | 32899190 |
| 23414 | 522145 | 1042632 | 2081196 | 4152623 | 8282205 | 16510899 | 32899195 |
| 14234 | 522145 | 1042632 | 2081196 | 4152623 | 8282206 | 16510902 | 32899203 |
| 14324 | 522145 | 1042632 | 2081196 | 4152623 | 8282206 | 16510902 | 32899205 |
| 14423 | 522145 | 1042632 | 2081196 | 4152623 | 8282207 | 16510909 | 32899236 |
| 14432 | 522145 | 1042632 | 2081196 | 4152623 | 8282207 | 16510909 | 32899239 |
| 34124 | 522145 | 1042632 | 2081197 | 4152627 | 8282220 | 16510941 | 32899295 | 65520977 |
| 34214 | 522145 | 1042632 | 2081197 | 4152627 | 8282220 | 16510941 | 32899295 | 65520976 |
| 12443,21443 | 522145 | 1042632 | 2081197 | 4152627 | 8282222 | 16510955 | 32899367 | 65521272 | 130420893 |
| 12434,21434 | 522145 | 1042632 | 2081197 | 4152627 | 8282222 | 16510955 | 32899367 | 65521272 | 130420894 |
| 41324 | 522145 | 1042632 | 2081197 | 4152628 | 8282227 | 16510978 |
| 42134 | 522145 | 1042632 | 2081197 | 4152628 | 8282227 | 16510979 |
| 41234 | 522145 | 1042632 | 2081197 | 4152628 | 8282228 |
| 23144 | 522145 | 1042632 | 2081197 | 4152628 | 8282229 | 16510991 | 32899515 | 65521811 | 130422680 | 259467469 | 515903007 |
| 31244 | 522145 | 1042632 | 2081197 | 4152628 | 8282229 | 16510991 | 32899515 | 65521811 | 130422680 | 259467469 | 515903012 |
| 12344,21344,32144 | 522145 | 1042632 | 2081197 | 4152628 | 8282229 | 16510991 | 32899515 | 65521811 | 130422684 | 259467492 | 515903117 |
| 13244 | 522145 | 1042632 | 2081197 | 4152628 | 8282229 | 16510991 | 32899515 | 65521811 | 130422684 | 259467492 | 515903121 |
| 24153 | 523194 | 1045321 | 2087895 | 4168924 | 8321100 | 16602179 | 33110392 |
| 31524 | 523194 | 1045321 | 2087895 | 4168924 | 8321100 | 16602179 | 33110393 |
| 25314 | 523194 | 1045321 | 2087895 | 4168924 | 8321100 | 16602179 | 33110394 |
| 24513 | 523194 | 1045321 | 2087895 | 4168924 | 8321100 | 16602179 | 33110395 |
| 14253 | 523194 | 1045321 | 2087895 | 4168924 | 8321100 | 16602180 | 33110398 |
| 13524 | 523194 | 1045321 | 2087895 | 4168924 | 8321100 | 16602180 | 33110400 | 66003540 | 131511362 |
| 25134 | 523194 | 1045321 | 2087895 | 4168924 | 8321100 | 16602180 | 33110400 | 66003540 | 131511361 |
| 13542 | 523194 | 1045321 | 2087895 | 4168924 | 8321100 | 16602180 | 33110401 | 66003546 | 131511390 |
| 14352 | 523194 | 1045321 | 2087895 | 4168924 | 8321100 | 16602180 | 33110401 | 66003546 | 131511391 |
| 25413 | 523194 | 1045321 | 2087895 | 4168924 | 8321100 | 16602180 | 33110404 |
| 23514 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602187 | 33110434 |
| 31425 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602187 | 33110436 | 66003689 |
| 24135 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602187 | 33110436 | 66003691 |
| 15324 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602188 | 33110440 | 66003703 |
| 32514 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602188 | 33110440 | 66003705 |
| 15234 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602188 | 33110441 | 66003711 |
| 14523 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602188 | 33110441 | 66003712 | 131511996 |
| 14532 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602188 | 33110441 | 66003712 | 131511998 |
| 15342 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602188 | 33110441 | 66003713 |
| 15243 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602188 | 33110442 | 66003716 |
| 14235 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602188 | 33110442 | 66003717 |
| 25143 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602188 | 33110442 | 66003719 | 131512031 |
| 15423 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602188 | 33110442 | 66003719 | 131512032 |
| 13425 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602188 | 33110442 | 66003719 | 131512033 |
| 32415 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602188 | 33110442 | 66003719 | 131512034 |
| 24315 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602188 | 33110442 | 66003721 |
| 13452 | 523194 | 1045321 | 2087895 | 4168924 | 8321101 | 16602188 | 33110443 |
| 12534,21534 | 523194 | 1045321 | 2087895 | 4168925 | 8321106 | 16602208 | 33110507 | 66003908 | 131512528 | 261908366 |
| 12453,21453 | 523194 | 1045321 | 2087895 | 4168925 | 8321106 | 16602208 | 33110507 | 66003908 | 131512528 | 261908367 |
| 35124 | 523194 | 1045321 | 2087895 | 4168925 | 8321106 | 16602207 | 33110499 | 66003865 | 131512342 |
| 35214 | 523194 | 1045321 | 2087895 | 4168925 | 8321106 | 16602207 | 33110499 | 66003865 | 131512341 |
| 42135 | 523194 | 1045321 | 2087895 | 4168925 | 8321107 | 16602215 | 33110544 | 66004065 | 131513117 |
| 41325 | 523194 | 1045321 | 2087895 | 4168925 | 8321107 | 16602215 | 33110544 | 66004065 | 131513119 |
| 23145,23154 | 523194 | 1045321 | 2087895 | 4168925 | 8321107 | 16602215 | 33110545 | 66004072 |
| 31245,31254 | 523194 | 1045321 | 2087895 | 4168925 | 8321107 | 16602215 | 33110545 | 66004073 |
| 34125 | 523194 | 1045321 | 2087895 | 4168925 | 8321107 | 16602216 | 33110550 | 66004092 | 131513218 | 261910724 | 521332661 |
| 34215 | 523194 | 1045321 | 2087895 | 4168925 | 8321107 | 16602216 | 33110550 | 66004092 | 131513218 | 261910724 | 521332662 |
| 41235 | 523194 | 1045321 | 2087895 | 4168925 | 8321107 | 16602216 | 33110550 | 66004092 | 131513218 | 261910721 |
| 42315 | 523194 | 1045321 | 2087895 | 4168925 | 8321107 | 16602216 | 33110550 | 66004093 |
| 23415 | 523194 | 1045321 | 2087895 | 4168925 | 8321107 | 16602216 | 33110550 | 66004094 | 131513234 |
| 43125 | 523194 | 1045321 | 2087895 | 4168925 | 8321107 | 16602216 | 33110550 | 66004094 | 131513235 |
| 12345,12354,12543 |
| 15432,21345,21354 | 523194 | 1045321 | 2087895 | 4168925 | 8321107 | 16602216 | 33110551 | 66004100 | 131513262 | 261910916 |
| 21543,32145,32154,43215 |
| 12435,21435 | 523194 | 1045321 | 2087895 | 4168925 | 8321107 | 16602216 | 33110551 | 66004100 | 131513262 | 261910917 |
| 14325 | 523194 | 1045321 | 2087895 | 4168925 | 8321107 | 16602216 | 33110551 | 66004100 | 131513263 |
| 13245,13254 | 523194 | 1045321 | 2087895 | 4168925 | 8321107 | 16602216 | 33110551 | 66004101 |