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Search: id:A092295
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| A092295 |
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Number of partitions of n with even number (or 0) 2's. |
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+0
4
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| 1, 1, 1, 2, 4, 5, 7, 10, 15, 20, 27, 36, 50, 65, 85, 111, 146, 186, 239, 304, 388, 488, 614, 767, 961, 1191, 1475, 1819, 2243, 2746, 3361, 4096, 4988, 6047, 7322, 8836, 10655, 12801, 15360, 18384, 21978, 26199, 31196, 37062, 43979, 52072, 61579, 72682
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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a(n) = A000041(n)-a(n-2).
G.f.=1/[(1+x^2)*product(1-x^j, j=1..infinity)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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EXAMPLE
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a(5)=5 because the partitions [5],[4,1],[3,1,1],[2,2,1], and [1,1,1,1,1] of 5 have an even number of 2's ([3,2] and [2,1,1,1] do not qualify).
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MAPLE
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g:=1/(1+x^2)/product(1-x^j, j=1..70): gser:=series(g, x=0, 50): seq(coeff(gser, x, n), n=0..47); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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CROSSREFS
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Cf. A087787.
Sequence in context: A018598 A018756 A018301 this_sequence A027936 A082741 A099522
Adjacent sequences: A092292 A092293 A092294 this_sequence A092296 A092297 A092298
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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), Feb 06 2004
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EXTENSIONS
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More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 08 2004
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