|A| = size of the alphabet, n = word length, k = factor length

Amounts of k-Abelian equivalency classes

|A| = 2   n  
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
  k   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
2 4 8 14 22 32 44 58 74 92 112 134 158 184 212 242 274 308 344 382 422 464 508 554 602 652 704 758 814 872
3 16 32 60 106 176 280 426 626 892 1238 1678 2230 2910 3738 4734 5920 7318 8954 10852 13040 15546 18400 21632 25276 29364
4 64 128 250 478 886 1590 2768 4680 7692 12326 19286 29524 44300 65256 94496 134710 189270 262374 359210 486124 650802 862534 1132430
5 256 512 1014 1992 3874 7438 14078 26266 48254 87298 155474 272578 470496 799794 1339378 2210844 3598784 5780204 9165504 14356150
6 1024 2048 4084 8122 16102 31786 62424 121904 236622 456326 873978 1661894 3136470 5873770 10912732 20110352
7 4096 8192 16366 32666 65130 129690 257832 511638 1013168 2001796 3945324 7755186
8 16384 32768 65514 130948 261650 522602 1043308 2081656 4150670
9 65536 131072 262116 524128 1047942 2095002
10 262144 524288 1048544

|A| = 3   n  
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
  k   1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231
2 9 27 75 186 414 840 1578 2784 4662 7476 11556 17313 25245 35955 50157 68697 92559
3 81 243 717 2073 5814 15774 41250 103842 251436 586056 1316847 2858295 6006132 12244842
4 729 2187 6543 19509 57879 170592 499032 1447080 4155384 11806146
5 6561 19683 59019 176871 529659 1584561 4734546
6 59049 177147 531405 1593975

|A| = 4   n  
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
  k   1 4 10 20 35 56 84 120 165 220 286 364 455 560 680 816 969
2 16 64 244 856 2728 7892 20876 51020 116408 250292 511196 998388 1874916
3 256 1024 4072 16060 62536 239728 902008 3323792 11971604
4 4096 16384 65500 261652 1044004 4159084
5 65536 262144 1048516

|A| = 5   n  
1 2 3 4 5 6 7 8 9 10 11 12 13
  k   1 5 15 35 70 126 210 330 495 715 1001 1365 1820 2380
2 25 125 605 2755 11615 44995 159955 523860 1591200 4516720 12070320
3 625 3125 15585 77425 382295 1872715 9084255
4 15625 78125 390565 1952065

Sizes of largest equivalency classes

|A| = 2   n  
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
  k   1 1 2 3 6 10 20 35 70 126 252 462 924 1716 3432 6435 12870 24310 48620 92378 184756 352716 705432 1352078 2704156 5200300 10400600 20058300 40116600 77558760 155117520 300540195
2 1 1 2 3 4 6 12 20 36 60 120 210 400 700 1400 2520 4900 8820 17640 32340 63504 116424 232848 432432 853776 1585584 3171168 5945940 11778624
3 1 1 2 3 4 6 9 12 20 36 60 90 144 240 432 720 1296 2400 4200 7200 14400 25200 48000 84000 160000
4 1 1 2 3 4 5 6 8 12 20 30 42 60 90 144 216 432 648 1020 1701 3024 5040 8100
5 1 1 2 3 4 5 6 7 9 12 20 30 42 56 72 90 135 189 270 378
6 1 1 2 3 4 5 6 7 8 9 12 20 30 42 56 72
7 1 1 2 3 4 5 6 7 8 9 10 12
8 1 1 2 3 4 5 6 7 8
9 1 1 2 3 4 5
10 1 1 2

|A| = 3   n  
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
  k   1 1 2 6 12 30 90 210 560 1680 4200 11550 34650 90090 252252 756756 2018016 5717712 17153136 46558512 133024320
2 1 1 2 3 6 12 20 36 90 180 450 900 2160 6480 15120 38880 97200
3 1 1 2 3 4 6 12 20 30 42 60 120 210 360
4 1 1 2 3 4 5 6 12 20 30
5 1 1 2 3 4 5 6
6 1 1 2 3

|A| = 4   n  
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
  k   1 1 2 6 24 60 180 630 2520 7560 25200 92400 369600 1201200 4204200 15765750 63063000
2 1 1 2 3 6 12 24 60 120 210 450 1152 3456
3 1 1 2 3 4 6 12 20 30
4 1 1 2 3 4 5
5 1 1 2

|A| = 5   n  
1 2 3 4 5 6 7 8 9 10 11 12 13
  k   1 1 2 6 24 120 360 1260 5040 22680 113400 415800 1663200 7207200
2 1 1 2 3 6 12 24 60 120 360 840
3 1 1 2 3 4 6 12
4 1 1 2 3