A301505 Expansion of Product_{k>=1} (1 + x^(4*k))*(1 + x^(4*k-1)).

1, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 3, 2, 0, 2, 5, 2, 0, 4, 7, 3, 1, 7, 10, 4, 2, 11, 14, 5, 4, 17, 19, 6, 8, 25, 25, 9, 13, 36, 33, 12, 21, 50, 43, 16, 33, 69, 55, 23, 49, 93, 70, 32, 71, 124, 89, 45, 102, 163, 112, 64, 142, 212, 141, 89, 195, 273, 177, 123, 265, 349

Offset

0,8

Comments

Number of partitions of n into distinct parts congruent to 0 or 3 mod 4.

Links

Table of n, a(n) for n=0..70.

Index entries for sequences related to partitions

Formula

G.f.: Product_{k>=1} (1 + x^A014601(k)).

a(n) ~ exp(Pi*sqrt(n/6)) / (2^(5/2)*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 23 2018

Example

a(11) = 3 because we have [11], [8, 3] and [7, 4].

Mathematica

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

Crossrefs

Cf. A014601, A035364, A035457, A131795, A147599, A301504, A301507, A301508.

Sequence in context: A136566 A330235 A048983 * A301504 A307432 A256140

Adjacent sequences: A301502 A301503 A301504 * A301506 A301507 A301508

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 22 2018

Status

approved