

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
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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)/(1x^(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



