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A168655 Number of compositions such that the number of parts is divisible by the first part. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A283818 A004039 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

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Last modified July 20 22:20 EDT 2019. Contains 325189 sequences. (Running on oeis4.)