A161051 Number of partitions of 2n into powers of two where every part appears at least twice.

0, 1, 1, 2, 1, 3, 2, 5, 3, 6, 5, 9, 6, 11, 9, 16, 11, 19, 16, 25, 19, 30, 25, 39, 30, 45, 39, 56, 45, 65, 56, 81, 65, 92, 81, 111, 92, 127, 111, 152, 127, 171, 152, 201, 171, 226, 201, 265, 226, 295, 265, 340, 295, 379, 340, 435, 379, 480, 435, 545, 480, 601, 545, 682, 601, 747

Offset

1,4

Comments

Number of partitions of n into powers of two where every part appears at least twice (=original definition), if 2^0 is accepted as a power of two. - R. H. Hardin, Jul 04 2009

Links

R. H. Hardin, Table of n, a(n) for n = 1..1000

Formula

G.f.: Product_{j>=1} (1 + x^(2*2^j)/(1 - x^(2^j))). - Emeric Deutsch, Jun 28 2009

Example

a(9)=3 because we have 444222, 4422222, and 2^9. - Emeric Deutsch, Jun 28 2009

Maple

g := product(1+x^(2*2^j)/(1-x^(2^j)), j = 1 .. 20): gser := series(g, x = 0, 145): seq(coeff(gser, x, 2*n), n = 1 .. 69); # Emeric Deutsch, Jun 28 2009

Crossrefs

Sequence in context: A045747 A308984 A029138 * A161255 A008731 A114209

Adjacent sequences: A161048 A161049 A161050 * A161052 A161053 A161054

Keyword

nonn

Author

R. H. Hardin, Jun 02 2009

Extensions

Definition corrected by Emeric Deutsch, Jun 28 2009

Status

approved