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

1,3

Links

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

Formula

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

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 *)

Crossrefs

Cf. A168659, A171632.

Sequence in context: A088551 A301903 A165660 * A107300 A285787 A047946

Adjacent sequences: A171631 A171632 A171633 * A171635 A171636 A171637

Keyword

easy,nonn

Author

Vladeta Jovovic, Dec 13 2009

Extensions

More terms from Alois P. Heinz, Dec 15 2009

Status

approved