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Search: id:A035362
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| A035362 |
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Number of partitions of n into parts 4k or 4k+1. |
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+0
1
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| 1, 1, 1, 2, 3, 3, 3, 5, 7, 8, 8, 11, 15, 17, 18, 23, 30, 35, 37, 45, 57, 66, 71, 84, 104, 121, 131, 151, 183, 212, 231, 263, 313, 362, 396, 446, 523, 601, 660, 738, 855, 979, 1076, 1196, 1372, 1562, 1719, 1903, 2164, 2454, 2701, 2979, 3363, 3795, 4177, 4594
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Also number of partitions of n such that number of 1's plus number of odd parts is greater than or equal to n. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 27 2006
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FORMULA
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G.f.=-1+1/[(1-x)product((1-x^(4j))(1-x^(4j+1)), j=1..infinity)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 07 2006
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EXAMPLE
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a(8)=5 because we have [8],[5,1,1,1],[4,4],[4,1,1,1,1], and [1,1,1,1,1,1,1,1].
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MAPLE
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g:=-1+1/(1-x)/product((1-x^(4*j))*(1-x^(4*j+1)), j=1..20): gser:=series(g, x=0, 60): seq(coeff(gser, x^n), n=1..56); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 07 2006
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CROSSREFS
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Adjacent sequences: A035359 A035360 A035361 this_sequence A035363 A035364 A035365
Sequence in context: A036020 A036024 A036029 this_sequence A042957 A131048 A126868
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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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