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Search: id:A118246
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| A118246 |
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Number of partitions of n such that even parts occur at most once and odd parts occur at most twice. |
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1
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| 1, 1, 2, 2, 3, 4, 6, 8, 10, 12, 16, 20, 26, 32, 40, 48, 59, 72, 88, 106, 128, 152, 182, 216, 258, 305, 360, 422, 496, 580, 680, 792, 922, 1068, 1238, 1432, 1656, 1908, 2196, 2520, 2892, 3312, 3792, 4330, 4940, 5624, 6400, 7272, 8258, 9361, 10602, 11988, 13548
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also number of partitions of n with no even multiples of 2 and no odd multiples of 3 (i.e. parts equal to 1 or 5 mod 6 and to 2 mod 4). Example: a(7)=8 because we have [7],[6,1],[5,2],[5,1,1],[2,2,2,1],[2,2,1,1,1],[2,1,1,1,1,1] and [1,1,1,1,1,1,1].
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 0..128 [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 13 2009]
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FORMULA
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G.f.=product((1+x^(2j-1)+x^(4j-2))(1+x^(2j)), j=1..infinity). G.f.=product([(1-x^(6j-3))(1-x^(4j))]/[(1-x^(2j-1))(1-x^(2j))],j=1..infinity). G.f.=1/product((1-x^(1+6j))(1-x^(5+6j))(1-x^(2+4j)), j=0..infinity).
G.f.=product((1+x^j)*(1+x^(2j))/(1+x^(3j)), j=1..infinity). [From Vladeta Jovovic (vladeta(AT)eunet.yu), Jul 24 2009]
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EXAMPLE
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a(7)=8 because we have [7],[6,1],[5,2],[5,1,1],[4,3],[4,2,1],[3,3,1] and [3,2,1,1].
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MAPLE
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g:=product((1+x^(2*j-1)+x^(4*j-2))*(1+x^(2*j)), j=1..50): gser:=series(g, x=0, 65): seq(coeff(gser, x, n), n=0..60);
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CROSSREFS
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Sequence in context: A005860 A114541 A077114 this_sequence A116902 A066447 A035542
Adjacent sequences: A118243 A118244 A118245 this_sequence A118247 A118248 A118249
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 18 2006
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