A132463 Number of partitions of n into distinct parts congruent to 0 or 1 modulo 3.

1, 1, 0, 1, 2, 1, 1, 3, 2, 2, 5, 4, 3, 7, 7, 5, 10, 11, 8, 14, 17, 13, 20, 25, 19, 27, 36, 29, 37, 50, 43, 51, 69, 61, 69, 94, 86, 93, 126, 120, 125, 167, 164, 167, 220, 222, 222, 287, 297, 294, 373, 393, 386, 481, 516, 505, 617, 672, 657, 788, 868, 850, 1002, 1114, 1094

Offset: 0

Author

Reinhard Zumkeller, Aug 22 2007

Keywords

• nonn

Examples

			a(7)=3 because we have 7, 61 and 43.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000 (first 201 terms from Reinhard Zumkeller)

Crossrefs

Cf. A032766, A035360, A003105, A132462.

Programs

Maple

g:=product((1+x^(3*k))*(1+x^(3*k-2)),k=1..30): gser:=series(g,x=0,100): seq(coeff(gser,x,n),n=0..65); # Emeric Deutsch, Aug 26 2007

Mathematica

nmax = 100; CoefficientList[Series[Product[((1+x^(3*k))*(1+x^(3*k-2))), {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-2)) ). - Emeric Deutsch, Aug 26 2007

a(n) ~ exp(Pi*sqrt(2*n)/3) / (2^(19/12) * sqrt(3) * n^(3/4)). - Vaclav Kotesovec, Aug 24 2015

Extensions

Prepended a(0) = 1, Joerg Arndt, Feb 22 2015