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

0,4

Links

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

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

Example

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).

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 *)

Crossrefs

Cf. A087787.

Sequence in context: A351390 A218074 A241735 * A277102 A168639 A275802

Adjacent sequences: A092292 A092293 A092294 * A092296 A092297 A092298

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 06 2004

Extensions

More terms from Benoit Cloitre, Feb 08 2004

Status

approved