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Search: id:A161051
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| A161051 |
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Number of partitions of 2n into powers of two where every part appears at least twice. |
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+0
1
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| 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; listen)
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OFFSET
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1,4
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COMMENT
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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. [From Ron Hardin (rhhardin(AT)att.net), Jul 04 2009]
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LINKS
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Ron Hardin, Table of n, a(n) for n=1..1000
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FORMULA
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G.f. = Product[1+x^{2*2^j}/(1-x^{2^j}), j=1..infinity]. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 28 2009]
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EXAMPLE
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a(9)=3 because we have 444222, 4422222, and 2^9. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 28 2009]
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MAPLE
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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); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 28 2009]
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CROSSREFS
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Sequence in context: A050360 A045747 A029138 this_sequence A161255 A008731 A114209
Adjacent sequences: A161048 A161049 A161050 this_sequence A161052 A161053 A161054
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KEYWORD
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nonn
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AUTHOR
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Ron Hardin (rhhardin(AT)att.net) Jun 02 2009
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EXTENSIONS
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Definition corrected by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 28 2009
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