A301568 Expansion of Product_{k>=1} (1 + x^(5*k))*(1 + x^(5*k-3)).

1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 1, 0, 3, 0, 2, 2, 0, 5, 0, 4, 2, 1, 7, 0, 7, 3, 2, 10, 0, 11, 4, 4, 14, 0, 17, 5, 8, 19, 1, 25, 6, 13, 25, 2, 36, 8, 21, 33, 4, 50, 10, 33, 43, 8, 69, 12, 49, 55, 14, 93, 16, 71, 70, 23, 124, 20, 102, 88, 37, 163, 26, 142, 110, 57, 212

Offset

0,8

Comments

Number of partitions of n into distinct parts congruent to 0 or 2 mod 5.

Links

Table of n, a(n) for n=0..74.

Index entries for sequences related to partitions

Formula

G.f.: Product_{k>=1} (1 + x^A047215(k)).

a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(33/20) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Mar 24 2018

Example

a(12) = 3 because we have [12], [10, 2] and [7, 5].

Mathematica

nmax = 74; CoefficientList[Series[Product[(1 + x^(5 k)) (1 + x^(5 k - 3)), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 74; CoefficientList[Series[x^3 QPochhammer[-1, x^5] QPochhammer[-x^(-3), x^5]/(2 (1 + x) (1 - x + x^2)), {x, 0, nmax}], x]
nmax = 74; CoefficientList[Series[Product[(1 + Boole[MemberQ[{0, 2}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A035368, A036822, A047215, A203776, A219607, A281272, A301562, A301563, A301564, A301565, A301567, A301569, A301570.

Sequence in context: A337048 A318051 A301569 * A036851 A036850 A260492

Adjacent sequences: A301565 A301566 A301567 * A301569 A301570 A301571

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 23 2018

Status

approved