A301569 Expansion of Product_{k>=1} (1 + x^(5*k))*(1 + x^(5*k-2)).

1, 0, 0, 1, 0, 1, 0, 0, 2, 0, 1, 1, 0, 3, 0, 2, 2, 0, 5, 0, 2, 4, 0, 7, 1, 3, 7, 0, 10, 2, 4, 11, 0, 14, 4, 5, 17, 0, 19, 8, 6, 25, 1, 25, 13, 8, 36, 2, 33, 21, 10, 50, 4, 43, 33, 12, 69, 8, 55, 49, 15, 93, 14, 70, 71, 19, 124, 23, 88, 102, 24, 163, 37, 110, 142, 31

Offset

0,9

Comments

Number of partitions of n into distinct parts congruent to 0 or 3 mod 5.

Links

Table of n, a(n) for n=0..75.

Index entries for sequences related to partitions

Formula

G.f.: Product_{k>=2} (1 + x^A047218(k)).

a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(37/20) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Mar 24 2018

Example

a(13) = 3 because we have [13], [10, 3] and [8, 5].

Mathematica

nmax = 75; CoefficientList[Series[Product[(1 + x^(5 k)) (1 + x^(5 k - 2)), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 75; CoefficientList[Series[x^2 QPochhammer[-1, x^5] QPochhammer[-x^(-2), x^5]/(2 (1 + x^2)), {x, 0, nmax}], x]
nmax = 75; CoefficientList[Series[Product[(1 + Boole[MemberQ[{0, 3}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A035369, A036822, A047218, A203776, A219607, A281271, A301562, A301563, A301564, A301565, A301567, A301568, A301570.

Sequence in context: A230426 A337048 A318051 * A301568 A036851 A036850

Adjacent sequences: A301566 A301567 A301568 * A301570 A301571 A301572

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 23 2018

Status

approved