A301504 Expansion of Product_{k>=1} (1 + x^(4*k))*(1 + x^(4*k-3)).

1, 1, 0, 0, 1, 2, 1, 0, 1, 3, 2, 0, 2, 5, 4, 1, 2, 7, 7, 2, 3, 10, 11, 4, 4, 14, 17, 8, 6, 19, 25, 13, 8, 25, 36, 21, 12, 33, 50, 33, 18, 43, 69, 49, 26, 56, 93, 71, 38, 72, 124, 102, 55, 92, 163, 142, 79, 118, 212, 195, 112, 151, 273, 265, 157, 193, 350, 354, 217, 246, 444

Offset

0,6

Comments

Number of partitions of n into distinct parts congruent to 0 or 1 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^A042948(k)).

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

Example

a(9) = 3 because we have [9], [8, 1] and [5, 4].

Mathematica

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

Crossrefs

Cf. A035362, A035451, A035457, A042948, A108932, A132463, A261734, A301505, A301507, A301508.

Sequence in context: A330235 A048983 A301505 * A307432 A256140 A321391

Adjacent sequences: A301501 A301502 A301503 * A301505 A301506 A301507

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 22 2018

Status

approved