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A161051 Number of partitions of 2n into powers of two where every part appears at least twice. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A176431 A045747 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

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Last modified July 21 19:25 EDT 2019. Contains 325199 sequences. (Running on oeis4.)