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
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Feb 06 2004
EXTENSIONS
More terms from Benoit Cloitre, Feb 08 2004
STATUS
approved