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Search: id:A118096
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| A118096 |
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Number of partitions of n such the largest part is twice the smallest part. |
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2
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| 0, 0, 1, 1, 2, 3, 3, 4, 6, 6, 6, 10, 9, 11, 13, 14, 15, 20, 18, 23, 25, 27, 27, 37, 35, 39, 43, 48, 49, 61, 57, 68, 72, 78, 81, 97, 95, 107, 114, 127, 128, 150, 148, 168, 179, 191, 198, 229, 230, 254, 266, 291, 300, 338, 344, 379, 398, 427, 444, 498, 505, 550, 580, 625
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Also number of partitions of n such that if the largest part occurs k times, then the number of parts is 2k. Example: a(8)=4 because we have [7,1],[6,2],[5,3], and [3,3,1,1].
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FORMULA
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G.f.=sum(x^(3k)/product(1-x^j, j=k..2k), k=1..infinity).
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EXAMPLE
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a(8)=4 because we have [4,2,2],[2,2,2,1,1],[2,2,1,1,1,1], and [2,1,1,1,1,1,1].
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MAPLE
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g:=sum(x^(3*k)/product(1-x^j, j=k..2*k), k=1..30): gser:=series(g, x=0, 75): seq(coeff(gser, x, n), n=1..70);
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CROSSREFS
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Sequence in context: A099072 A106464 A093003 this_sequence A145806 A100989 A023158
Adjacent sequences: A118093 A118094 A118095 this_sequence A118097 A118098 A118099
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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 12 2006
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