A321038
Number of words of length 3n such that all letters of the octonary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting triples of identical letters into the initially empty word.
Original entry on oeis.org
43263, 7104240, 694377450, 52825297536, 3463906615356, 206132702914710, 11470240358743842, 608199451197152100, 31120996552066805175, 1550313320809537870320, 75665062766954753664390, 3635046065217379316477688, 172499755061750807257325550
Offset: 8
-
b:= (n, k)-> `if`(n=0, 1, k/n*add(binomial(3*n, j)*(n-j)*(k-1)^j, j=0..n-1)):
a:= n-> (k-> add((-1)^i*b(n, k-i)/(i!*(k-i)!), i=0..k))(8):
seq(a(n), n=8..25);
A321039
Number of words of length 3n such that all letters of the nonary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting triples of identical letters into the initially empty word.
Original entry on oeis.org
246675, 52676325, 6567205788, 627427976340, 51015901999920, 3724987212716133, 252083271295845990, 16134288197281838562, 990146359650754095405, 58830559749207291469515, 3408249740757631887365820, 193544431133535679583811150, 10816879949695374764949152976
Offset: 9
-
b:= (n, k)-> `if`(n=0, 1, k/n*add(binomial(3*n, j)*(n-j)*(k-1)^j, j=0..n-1)):
a:= n-> (k-> add((-1)^i*b(n, k-i)/(i!*(k-i)!), i=0..k))(9):
seq(a(n), n=9..25);
A321040
Number of words of length 3n such that all letters of the denary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting triples of identical letters into the initially empty word.
Original entry on oeis.org
1430715, 385671000, 59757446980, 7005490433656, 691555233881785, 60757817462444531, 4909804407096952946, 372791285261732999200, 26986460830582840320825, 1882051044395835159556710, 127426007577261157375345878, 8424538202077517861490125956
Offset: 10
-
b:= (n, k)-> `if`(n=0, 1, k/n*add(binomial(3*n, j)*(n-j)*(k-1)^j, j=0..n-1)):
a:= n-> (k-> add((-1)^i*b(n, k-i)/(i!*(k-i)!), i=0..k))(10):
seq(a(n), n=10..25);
A321041
Number of words of length 6n such that all letters of the n-ary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting triples of identical letters into the initially empty word.
Original entry on oeis.org
1, 1, 97, 29886, 16482191, 13337746758, 14329297278912, 19256258184412314, 31120996552066805175, 58830559749207291469515, 127426007577261157375345878, 311250333529456439224989700168, 846594239519776323268829614117536, 2538054216720547203941994076323844425
Offset: 0