A293583 Number of compositions of n where each part i is marked with a word of length i over a senary alphabet whose letters appear in alphabetical order and all six letters occur at least once in the composition.

4683, 155928, 3116220, 48697048, 657516672, 8065687344, 92540869002, 1011476639976, 10662168594984, 109327852591208, 1097238662684028, 10827944900524680, 105430826499237004, 1015590292306277376, 9698300806656595584, 91961212434214073824, 866974686508851897168

Offset: 6

Author

Alois P. Heinz, Oct 12 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..1000

Crossrefs

Column k=6 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))(6):
seq(a(n), n=6..30);

Formula

a(n) = 42*a(n-1) - 770*a(n-2) + 8190*a(n-3) - 56854*a(n-4) + 275758*a(n-5) - 980010*a(n-6) + 2645668*a(n-7) - 5576808*a(n-8) + 9366788*a(n-9) - 12715312*a(n - 10) + 14078260*a(n - 11) - 12772248*a(n - 12) + 9499064*a(n - 13) - 5769584*a(n - 14) + 2837496*a(n - 15) - 1113568*a(n - 16) + 340784*a(n - 17) - 78416*a(n - 18) + 12768*a(n - 19) - 1312*a(n - 20) + 64*a(n - 21). - Vaclav Kotesovec, Oct 14 2017