A130711 Number of compositions of n such that the smallest part divides every part.

1, 2, 4, 8, 14, 32, 57, 123, 239, 493, 970, 1997, 3953, 8017, 16024, 32281, 64550, 129742, 259561, 520606, 1041871, 2087177, 4176594, 8362063, 16730862, 33483361, 66987710, 134029333, 268117646, 536373213, 1072909785, 2146169660

Offset

1,2

Links

Table of n, a(n) for n=1..32.

Formula

Inverse Moebius transform of A099036.

G.f.: Sum_{n>0} x^n*(1-x^n)^2/((1-2*x^n)*(1-x^n-x^(2*n))).

Example

a(5)=14 because among the 16 compositions of 5 only 2+3 and 3+2 do not qualify; the others, except for the composition 5, have at least one component equal to 1.

Maple

G:=sum(x^n*(1-x^n)^2/((1-2*x^n)*(1-x^n-x^(2*n))), n=1..50); Gser:=series(G, x =0, 40): seq(coeff(Gser, x, n), n=1..33); # Emeric Deutsch, Sep 08 2007

Crossrefs

Cf. A083710.

Sequence in context: A038024 A337500 A061297 * A355189 A093483 A028398

Adjacent sequences: A130708 A130709 A130710 * A130712 A130713 A130714

Keyword

easy,nonn

Author

Vladeta Jovovic, Jul 01 2007

Extensions

More terms from Emeric Deutsch, Sep 08 2007

Status

approved