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

Author

Joerg Arndt and Alois P. Heinz, Apr 26 2014

Keywords

• nonn

Examples

			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].
		

Links

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

Crossrefs

Column k=6 of A238343 and of A238344.

Programs

Maple

b:= proc(n, i) option remember;
      `if`(n=0, 1, convert(series(add(b(n-j, j)*
      `if`(j 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 *)