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

0,5

Links

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

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

Example

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

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 *)

Crossrefs

Cf. A032766, A035360, A003105, A132462.

Sequence in context: A132462 A161039 A104467 * A153901 A132844 A006843

Adjacent sequences: A132460 A132461 A132462 * A132464 A132465 A132466

Keyword

nonn

Author

Reinhard Zumkeller, Aug 22 2007

Extensions

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

Status

approved