A105205 G.f.: Sum((1-x)^(2*l)*Sum(x^((2*l-1)*k)/(1-2*x+x^k)^(2*l),k=1..infinity),l=1..infinity).

1, 1, 4, 6, 13, 24, 51, 101, 205, 407, 814, 1624, 3248, 6490, 12979, 25950, 51898, 103798, 207619, 415288, 830690, 1661590, 3323566, 6647779, 13296602, 26594769, 53191708, 106386020, 212774300, 425548246, 851088094, 1702147791, 3404222451

Offset

1,3

Links

Table of n, a(n) for n=1..33.

Formula

Number of compositions of n such that the greatest part occurs with odd multiplicity.

Example

a(4)=6 because we have (4),(3,1),(1,3),(2,1,1),(1,2,1) and (1,1,2).

Maple

G:=sum((1-x)^(2*l)*sum(x^((2*l-1)*k)/(1-2*x+x^k)^(2*l), k=1..30), l=1..20): Gser:=series(G, x=0, 35): seq(coeff(Gser, x^n), n=1..33); # Emeric Deutsch, Jun 07 2005

Crossrefs

Cf. A105201, A105200.

Sequence in context: A049732 A262194 A136391 * A302311 A160805 A359020

Adjacent sequences: A105202 A105203 A105204 * A105206 A105207 A105208

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 12 2005

Extensions

More terms from Emeric Deutsch, Jun 07 2005

Status

approved