A168655 Number of compositions such that the number of parts is divisible by the first part.

1, 1, 3, 5, 11, 22, 44, 88, 177, 355, 710, 1419, 2838, 5679, 11363, 22727, 45443, 90862, 181703, 363419, 726903, 1453875, 2907667, 5814880, 11628864, 23256828, 46513965, 93031069, 186068503, 372142797, 744280096, 1488527555, 2976987042, 5953897971, 11907811651

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..250

Formula

G.f.: (1-x)*Sum(x^(2*n-1)/((1-x)^n-x^n),n=1..infinity), First differences of A101510.

a(n) ~ log(2) * 2^(n-1). - Vaclav Kotesovec, May 01 2014

Maple

b:= proc(n, t, g) option remember; `if`(n=0,
      `if`(irem(t, g)=0, 1, 0), add(b(n-i, t+1,
      `if`(g=0, 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

A101510[n_] := Sum[If[Mod[i+1, k+1] == 0, Binomial[n-k, i], 0], {k, 0, n/2}, {i, 0, n-k}]; A168655 =  Join[{1}, Table[A101510[n], {n, 0, 32}] // Differences] (* Jean-François Alcover, Jan 24 2014 *)

Crossrefs

Cf. A079501.

Sequence in context: A004039 A341532 A293338 * A005830 A007008 A018110

Adjacent sequences: A168652 A168653 A168654 * A168656 A168657 A168658

Keyword

easy,nonn

Author

Vladeta Jovovic, Dec 01 2009

Extensions

More terms from Alois P. Heinz, Dec 15 2009

Status

approved