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A168655 Number of compositions such that the number of parts is divisible by the first part. 6

%I

%S 1,1,3,5,11,22,44,88,177,355,710,1419,2838,5679,11363,22727,45443,

%T 90862,181703,363419,726903,1453875,2907667,5814880,11628864,23256828,

%U 46513965,93031069,186068503,372142797,744280096,1488527555,2976987042,5953897971,11907811651

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

%H Alois P. Heinz, <a href="/A168655/b168655.txt">Table of n, a(n) for n = 1..250</a>

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

%F a(n) ~ log(2) * 2^(n-1). - _Vaclav Kotesovec_, May 01 2014

%p b:= proc(n,t,g) option remember; `if`(n=0,

%p `if`(irem(t, g)=0, 1, 0), add(b(n-i, t+1,

%p `if`(g=0,i,g)), i=1..n))

%p end:

%p a:= n-> b(n,0,0):

%p seq(a(n), n=1..40); # _Alois P. Heinz_, Dec 15 2009

%t 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-Fran├žois Alcover_, Jan 24 2014 *)

%Y Cf. A079501.

%K easy,nonn

%O 1,3

%A _Vladeta Jovovic_, Dec 01 2009

%E More terms from _Alois P. Heinz_, Dec 15 2009

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Last modified July 27 01:40 EDT 2021. Contains 346302 sequences. (Running on oeis4.)