A006477 - OEIS

%I M3232 #22 Mar 17 2014 10:41:12

%S 0,0,0,1,1,4,4,10,11,22,25,44,51,83,98,149,177,259,309,436,521,716,

%T 857,1151,1376,1816,2170,2818,3361,4309,5132,6502,7728,9695,11501,

%U 14298,16924,20877,24661,30203,35598,43323,50956,61651,72357,87086,101999

%N Number of partitions of n with at least 1 odd and 1 even part.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A006477/b006477.txt">Table of n, a(n) for n = 0..1000</a>

%H M. O. LeVan, <a href="http://www.jstor.org/stable/2317572">A triangle for partitions</a>, Amer. Math. Monthly, 79 (1972), 507-510.

%F 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).

%F G.f.: (prod(1/(1-x^k), k odd)-1) * (prod(1/(1-x^k), k even)-1).

%F A000041(n)-A000009(n) if n is odd else A000041(n)-A000009(n)-A000041(n/2). - _Vladeta Jovovic_, Sep 10 2003

%F a(n) = A000041(n) - A096441(n), n >= 1. - _Omar E. Pol_, Aug 16 2013

%t 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_ *)

%Y Cf. A047967, A038348.

%K nonn

%O 0,6

%A _N. J. A. Sloane_.

%E More terms from _David W. Wilson_, May 11 2001