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 A006477 Number of partitions of n with at least 1 odd and 1 even part. (Formerly M3232) 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS 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. FORMULA 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 MATHEMATICA 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 *) CROSSREFS Cf. A047967, A038348. Sequence in context: A188271 A219939 A219471 * A233739 A279036 A182699 Adjacent sequences:  A006474 A006475 A006476 * A006478 A006479 A006480 KEYWORD nonn AUTHOR EXTENSIONS More terms from David W. Wilson, May 11 2001 STATUS approved

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Last modified May 30 18:38 EDT 2020. Contains 334728 sequences. (Running on oeis4.)