A035360 Number of partitions of n into parts 3k or 3k+1.

1, 1, 1, 2, 3, 3, 5, 7, 8, 11, 15, 17, 23, 30, 35, 44, 57, 66, 82, 103, 121, 146, 181, 211, 253, 308, 360, 425, 513, 596, 700, 834, 969, 1127, 1333, 1541, 1786, 2093, 2415, 2781, 3241, 3723, 4273, 4946, 5669, 6476, 7461, 8519, 9705, 11123, 12669, 14379, 16418

Offset: 0

Author

Olivier Gérard

Keywords

• nonn

Comments

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

Examples

			1 + x + x^2 + 2*x^3 + 3*x^4 + 3*x^5 + 5*x^6 + 7*x^7 + 8*x^8 + 11*x^9 + ...
		

Links

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

Crossrefs

Cf. A032766, A132463, A000726, A035361.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[1/((1 - x^(3*k))*(1 - x^(3*k-2))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 23 2015 *)
nmax = 52; kmax = nmax/3;
s = Flatten[{Range[0, kmax]*3}~Join~{Range[0, kmax]*3 + 1}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 0, nmax}] (* Robert Price, Aug 02 2020 *)

Formula

a(n) ~ Gamma(1/3) * exp(2*Pi*sqrt(n)/3) / (4 * sqrt(3) * Pi^(2/3) * n^(11/12)). - Vaclav Kotesovec, Aug 23 2015