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Search: id:A118267
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| A118267 |
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Number of partitions of n such that if the smallest part is k, then both k and k+1 occur exactly once. |
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| 0, 0, 1, 0, 1, 1, 2, 1, 4, 3, 5, 6, 9, 9, 15, 15, 22, 26, 34, 38, 53, 60, 77, 91, 115, 133, 170, 196, 243, 287, 349, 408, 500, 582, 701, 822, 984, 1147, 1371, 1594, 1889, 2204, 2596, 3014, 3549, 4111, 4812, 5576, 6502, 7512, 8744, 10081, 11691, 13470, 15573, 17898
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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Also number of partitions of n such that if the largest part is k, then k-1 occurs exactly once and k-2 also occurs (0 is considered to be a part of each partition). Example: a(11)=5 because we have [4,3,2,2],[4,3,2,1,1],[3,3,2,1,1,1],[2,2,2,2,2,1], and [3,2,1,1,1,1,1,1].
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FORMULA
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G.f.=sum(x^(2k+1)/product(1-x^j, j=k+2..infinity), k=1..infinity). G.f.=sum(x^(3k-3)/[(1-x^k)*product(1-x^j, j=1..k-2)], k=2..infinity).
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EXAMPLE
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a(11)=5 because we have [8,2,1],[6,5],[6,3,2],[5,3,2,1], and [4,4,2,1].
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MAPLE
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g:=sum(x^(3*k-3)/(1-x^k)/product(1-x^j, j=1..k-2), k=2..30): gser:=series(g, x, 65): seq(coeff(gser, x, n), n=1..62);
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CROSSREFS
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Sequence in context: A107640 A030065 A055176 this_sequence A075348 A055631 A004560
Adjacent sequences: A118264 A118265 A118266 this_sequence A118268 A118269 A118270
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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 20 2006
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