A293585 Number of compositions of n where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order and all eight letters occur at least once in the composition.

545835, 30532384, 984910128, 24082101504, 496274574936, 9104663637024, 153620123190816, 2434519831873920, 36763980389367378, 534505149483841568, 7538836344403305280, 103747819539055788640, 1399283448432865901624, 18560930972118370361856

Offset: 8

Author

Alois P. Heinz, Oct 12 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..925

Crossrefs

Column k=8 of A261781.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1,
      add(b(n-j, k)*binomial(j+k-1, k-1), j=1..n))
    end:
a:= n-> (k->add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k))(8):
seq(a(n), n=8..30);

Formula

a(n) = 72*a(n-1) - 2352*a(n-2) + 46452*a(n-3) - 624540*a(n-4) + 6112176*a(n-5) - 45535444*a(n-6) + 266958678*a(n-7) - 1264269754*a(n-8) + 4940034192*a(n-9) - 16203617768*a(n - 10) + 45247660712*a(n - 11) - 108803821608*a(n - 12) + 227386203188*a(n - 13) - 416072786528*a(n - 14) + 670510739364*a(n - 15) - 955987452656*a(n - 16) + 1210032902216*a(n - 17) - 1363000899064*a(n - 18) + 1368396317120*a(n - 19) - 1225293972272*a(n - 20) + 978413136792*a(n - 21) - 696053259552*a(n - 22) + 440365848816*a(n - 23) - 247084003008*a(n - 24) + 122486489680*a(n - 25) - 53377923152*a(n - 26) + 20315614688*a(n - 27) - 6696256832*a(n - 28) + 1890687584*a(n - 29) - 450764768*a(n - 30) + 89006080*a(n - 31) - 14167936*a(n - 32) + 1747264*a(n - 33) - 156672*a(n - 34) + 9088*a(n - 35) - 256*a(n - 36). - Vaclav Kotesovec, Oct 14 2017