A092295 Number of partitions of n with even number (or 0) 2's.

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

Offset: 0

Author

Vladeta Jovovic, Feb 06 2004

Keywords

• easy
• nonn

Examples

			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).
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A087787.

Programs

Maple

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, Mar 30 2006

Mathematica

nmax = 50; CoefficientList[Series[1/((1+x^2) * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 30 2015 *)

Formula

a(n) = A000041(n)-a(n-2).

G.f.=1/[(1+x^2)*product(1-x^j, j=1..infinity)]. - Emeric Deutsch, Mar 30 2006

a(n) ~ exp(Pi*sqrt(2*n/3)) / (8*n*sqrt(3)). - Vaclav Kotesovec, Oct 30 2015

Extensions

More terms from Benoit Cloitre, Feb 08 2004