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A006477
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Number of partitions of n with at least 1 odd and 1 even part.
(Formerly M3232)
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6
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0, 0, 0, 1, 1, 4, 4, 10, 11, 22, 25, 44, 51, 83, 98, 149, 177, 259, 309, 436, 521, 716, 857, 1151, 1376, 1816, 2170, 2818, 3361, 4309, 5132, 6502, 7728, 9695, 11501, 14298, 16924, 20877, 24661, 30203, 35598, 43323, 50956, 61651, 72357, 87086, 101999
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OFFSET
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0,6
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1000
M. O. LeVan, A triangle for partitions, Amer. Math. Monthly, 79 (1972), 507-510.
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FORMULA
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Convolution of 0, 1, 1, 2, 2, 3, 4, 5, 6, ... (essentially A000009) and 0, 0, 1, 0, 2, 0, 3, 0, 5, ... (essentially A035363).
G.f.: (prod(1/(1-x^k), k odd)-1) * (prod(1/(1-x^k), k even)-1).
A000041(n)-A000009(n) if n is odd else A000041(n)-A000009(n)-A000041(n/2). - Vladeta Jovovic, Sep 10 2003
a(n) = A000041(n) - A096441(n), n >= 1. - Omar E. Pol, Aug 16 2013
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MATHEMATICA
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a[n_?OddQ] := PartitionsP[n] - PartitionsQ[n]; a[n_?EvenQ] := PartitionsP[n] - PartitionsQ[n] - PartitionsP[n/2]; a[0] = 0; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Mar 17 2014, after Vladeta Jovovic *)
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CROSSREFS
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Cf. A047967, A038348.
Sequence in context: A188271 A219939 A219471 * A233739 A279036 A182699
Adjacent sequences: A006474 A006475 A006476 * A006478 A006479 A006480
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from David W. Wilson, May 11 2001
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STATUS
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approved
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