A035361 Number of partitions of n into parts 3k or 3k+2.

1, 0, 1, 1, 1, 2, 3, 2, 5, 5, 6, 9, 11, 11, 18, 19, 23, 31, 36, 40, 56, 60, 73, 92, 105, 121, 155, 170, 204, 247, 280, 325, 397, 440, 521, 615, 695, 805, 954, 1063, 1244, 1442, 1626, 1873, 2176, 2431, 2813, 3221, 3623, 4146, 4751, 5309, 6086, 6905, 7746, 8807

Offset: 0

Author

Olivier Gérard

Keywords

• nonn

Comments

Euler transform of period 3 sequence [ 0, 1, 1, ...]. - Kevin T. Acres, Apr 28 2018

Examples

			1 + x^2 + x^3 + x^4 + 2*x^5 + 3*x^6 + 2*x^7 + 5*x^8 + 5*x^9 + 6*x^10 + ...
		

Links

• Robert Price, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A007494, A132462, A000726, A035360.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[1/((1 - x^(3*k))*(1 - x^(3*k-1))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 23 2015 *)
nmax = 55; kmax = nmax/3;
s = Flatten[{Range[0, kmax]*3}~Join~{Range[0, kmax]*3 + 2}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 0, nmax}] (* Robert Price, Aug 02 2020 *)

Formula

a(n) ~ Gamma(2/3) * exp(2*Pi*sqrt(n)/3) / (4 * sqrt(3) * n^(13/12) * Pi^(1/3)). - Vaclav Kotesovec, Aug 23 2015