A132462 Number of partitions of n into distinct parts congruent to 0 or 2 modulo 3.

1, 0, 1, 1, 0, 2, 1, 1, 3, 2, 2, 5, 2, 4, 7, 4, 7, 10, 6, 11, 14, 9, 17, 19, 14, 25, 26, 21, 36, 35, 31, 50, 47, 45, 69, 63, 64, 93, 84, 89, 125, 111, 124, 165, 147, 169, 216, 194, 227, 281, 254, 303, 363, 332, 400, 466, 432, 523, 595, 559, 680, 756, 721, 876, 956, 926, 1121

Offset: 0

Author

Reinhard Zumkeller, Aug 22 2007

Keywords

• nonn

Examples

			a(8)=3 because we have 8, 6+2 and 5+3.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A007494, A035361, A003105, A132463.

Programs

Maple

g:=product((1+x^(3*k))*(1+x^(3*k-1)),k=1..30): gser:=series(g,x=0,100): seq(coeff(gser,x,n),n=0..70); # Emeric Deutsch, Aug 30 2007

Mathematica

nmax = 40; CoefficientList[Series[Product[((1+x^(3*k))*(1+x^(3*k-1))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 24 2015 *)

Formula

G.f.: Product_{k>=1} (1+x^(3*k))*(1+x^(3*k-1)). - Emeric Deutsch, Aug 30 2007

a(n) ~ exp(Pi*sqrt(2*n)/3) / (2^(23/12) * sqrt(3) * n^(3/4)). - Vaclav Kotesovec, Aug 24 2015

Extensions

a(0)=1 prepended by Vaclav Kotesovec, Aug 24 2015