A171634 Number of compositions of n such that the number of parts is divisible by the greatest part.

1, 1, 3, 2, 8, 13, 21, 38, 89, 173, 302, 545, 1109, 2309, 4564, 8601, 16188, 31365, 62518, 125813, 251119, 493123, 956437, 1854281, 3633938, 7218166, 14444539, 28868203, 57300450, 112921744, 221760513, 436117749, 861764899, 1711773936

Offset: 1

Author

Vladeta Jovovic, Dec 13 2009

Keywords

• easy
• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..715 (terms 1..250 from Alois P. Heinz)

Crossrefs

Cf. A168659, A171632.

Programs

Maple

b:= proc(n,t,g) option remember; `if`(n=0, `if`(irem(t, g)=0, 1, 0), add(b(n-i, t+1, max(i, g)), i=1..n)) end: a:= n-> b(n,0,0): seq(a(n), n=1..40); # Alois P. Heinz, Dec 15 2009

Mathematica

b[n_, t_, g_] := b[n, t, g] = If[n == 0, If [Mod[t, g] == 0, 1, 0], Sum[b[n - i, t + 1, Max[i, g]], {i, 1, n}]];
a[n_] := b[n, 0, 0];
Array[a, 40] (* Jean-François Alcover, Nov 11 2020, after Alois P. Heinz *)

Formula

G.f.: Sum_{n>=0} Sum_{d|n} ((x^(d+1)-x)^n-(x^d-x)^n)/(x-1)^n.

Extensions

More terms from Alois P. Heinz, Dec 15 2009