A241631 Number of compositions of n with exactly six descents.

13, 139, 927, 4719, 20122, 75317, 254805, 794475, 2315005, 6369689, 16681342, 41842970, 101039601, 235855414, 534058830, 1176497139, 2527742988, 5308195367, 10915439320, 22015220687, 43612884462, 84970442998, 162994589899, 308155639555, 574716486444

Offset

18,1

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 18..1000

Example

a(18) = 13: [3,2,1,3,2,1,3,2,1], [2,1,3,2,1,3,2,1,2,1], [2,1,2,1,3,2,1,3,2,1], [3,2,1,3,2,1,2,1,2,1], [2,1,3,2,1,2,1,3,2,1], [3,2,1,2,1,2,1,3,2,1], [3,2,1,2,1,3,2,1,2,1], [2,1,2,1,2,1,3,2,1,2,1], [2,1,2,1,3,2,1,2,1,2,1], [2,1,3,2,1,2,1,2,1,2,1], [2,1,2,1,2,1,2,1,3,2,1], [3,2,1,2,1,2,1,2,1,2,1], [2,1,2,1,2,1,2,1,2,1,2,1].

Maple

b:= proc(n, i) option remember;
      `if`(n=0, 1, convert(series(add(b(n-j, j)*
      `if`(j<i, x, 1), j=1..n), x, 7), polynom))
    end:
a:= n-> coeff(b(n, 0), x, 6):
seq(a(n), n=18..50);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[b[n-j, j]*
   If[j < i, x, 1], {j, 1, n}] // Expand];
a[n_] := Coefficient[b[n, 0], x, 6];
Table[a[n], {n, 18, 50}] (* Jean-François Alcover, Nov 28 2023, from Maple code *)

Crossrefs

Column k=6 of A238343 and of A238344.

Sequence in context: A280745 A142896 A193700 * A125425 A016145 A351812

Adjacent sequences: A241628 A241629 A241630 * A241632 A241633 A241634

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 26 2014

Status

approved