A301508 Expansion of Product_{k>=0} (1 + x^(4*k+2))*(1 + x^(4*k+3)).

1, 0, 1, 1, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 3, 4, 4, 5, 5, 6, 7, 6, 8, 9, 9, 11, 12, 13, 14, 15, 17, 19, 20, 23, 25, 27, 29, 31, 35, 37, 40, 46, 48, 52, 57, 60, 66, 71, 76, 85, 90, 97, 105, 112, 121, 129, 140, 152, 161, 174, 187, 198, 214, 228, 245, 265, 280, 302, 323, 342

Offset: 0

Author

Ilya Gutkovskiy, Mar 22 2018

Keywords

• nonn

Comments

Number of partitions of n into distinct parts congruent to 2 or 3 mod 4.

Examples

			a(13) = 3 because we have [11, 2], [10, 3] and [7, 6].
		

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A035366, A042964, A070048, A131795, A147599, A301504, A301505, A301507.

Programs

Mathematica

nmax = 70; CoefficientList[Series[Product[(1 + x^(4 k + 2)) (1 + x^(4 k + 3)), {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 70; CoefficientList[Series[QPochhammer[-x^2, x^4] QPochhammer[-x^3, x^4], {x, 0, nmax}], x]
nmax = 70; CoefficientList[Series[Product[(1 + Boole[MemberQ[{2, 3}, Mod[k, 4]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} (1 + x^A042964(k)).

a(n) ~ exp(Pi*sqrt(n/6)) / (4*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 23 2018