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Search: id:A096778
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| A096778 |
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Number of partitions of n with at most two even parts. |
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+0
1
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| 1, 1, 2, 3, 5, 7, 10, 14, 19, 26, 34, 45, 58, 75, 95, 121, 151, 189, 234, 289, 354, 433, 526, 637, 768, 923, 1105, 1319, 1569, 1861, 2202, 2597, 3056, 3587, 4201, 4908, 5723, 6658, 7732, 8961, 10367, 11971, 13802, 15884, 18253, 20942, 23992, 27445, 31353
(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+4 with exactly two even parts. Example: a(3)=3 because the partitions of 7 with exactly two even parts are [4,2,1], [3,2,2], and [2,2,1,1,1]. a(n)=A116482(n+4,2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 21 2006
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FORMULA
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G.f.: (1/((1-x^2)*(1-x^4)))/Product(1-x^(2*i+1), i=0..infinity).More generally, g.f. for number of partitions of n with at most k even parts is (1/Product(1-x^(2*i), i=1..k))/Product(1-x^(2*i+1), i=0..infinity).
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EXAMPLE
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a(3)=3 because we have [3],[2,1], and [1,1,1].
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MATHEMATICA
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CoefficientList[ Series[(1/((1 - x^2)*(1 - x^4)))/Product[1 - x^(2i + 1), {i, 0, 50}], {x, 0, 48}], x] (from Robert G. Wilson v Aug 16 2004)
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CROSSREFS
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Cf. A038348.
Cf. A116482.
Adjacent sequences: A096775 A096776 A096777 this_sequence A096779 A096780 A096781
Sequence in context: A036469 A116480 A023026 this_sequence A102108 A105780 A001522
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 16 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 17 2004
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 21 2006
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