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Search: id:A035462
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| A035462 |
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Number of partitions of n into parts 4k-1. |
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+0
3
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| 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 1, 2, 3, 2, 2, 4, 4, 3, 4, 5, 5, 5, 6, 7, 8, 7, 8, 11, 10, 10, 13, 14, 14, 15, 17, 19, 20, 20, 24, 27, 26, 28, 33, 35, 35, 39, 44, 46, 48, 52, 58, 62, 63, 69, 78, 80, 83, 93, 100, 104, 111, 120, 130, 137, 143, 156, 169, 175, 185, 203
(list; graph; listen)
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OFFSET
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1,14
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COMMENT
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Also, number of partitions into parts 8k+3 or 8k+7.
Also number of partitions of n such that 2k-1 and 2k occur with the same multiplicity. Example: a(18)=3 because we have [8,7,2,1],[6,5,4,3], and [2,2,2,2,2,2,1,1,1,1,1,1]. It is easy to find a bijection between these partitions and those described in the definition. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 05 2006
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FORMULA
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G.f.=-1+1/product(1-x^(4i-1), i=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 05 2006
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EXAMPLE
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a(18)=3 because we have [15,3],[11,7], and [3,3,3,3,3,3].
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MAPLE
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g:=-1+1/product(1-x^(4*i-1), i=1..50): gser:=series(g, x=0, 80): seq(coeff(gser, x, n), n=1..75); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 05 2006
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CROSSREFS
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Cf. A035441-A035468.
Sequence in context: A090970 A091972 A025833 this_sequence A120481 A029291 A022872
Adjacent sequences: A035459 A035460 A035461 this_sequence A035463 A035464 A035465
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KEYWORD
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nonn
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AUTHOR
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Olivier Gerard (ogerard(AT)ext.jussieu.fr)
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