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

0,6

Links

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

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

Example

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

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 *)

Crossrefs

Cf. A007494, A035361, A003105, A132463.

Sequence in context: A228668 A058636 A226009 * A161039 A104467 A132463

Adjacent sequences: A132459 A132460 A132461 * A132463 A132464 A132465

Keyword

nonn

Author

Reinhard Zumkeller, Aug 22 2007

Extensions

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

Status

approved