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

6,1

Links

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

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

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);

Crossrefs

Column k=6 of A261781.

Sequence in context: A226801 A320620 A218096 * A263066 A252773 A368192

Adjacent sequences: A293580 A293581 A293582 * A293584 A293585 A293586

Keyword

nonn

Author

Alois P. Heinz, Oct 12 2017

Status

approved