A301565 Expansion of Product_{k>=0} (1 + x^(5*k+3))*(1 + x^(5*k+4)).

1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 2, 2, 1, 1, 2, 3, 2, 1, 2, 4, 4, 3, 3, 4, 6, 6, 4, 4, 7, 9, 7, 6, 8, 11, 12, 10, 9, 12, 16, 16, 14, 14, 19, 23, 22, 19, 21, 27, 31, 29, 26, 31, 40, 42, 38, 38, 45, 53, 55, 51, 52, 63, 73, 73, 69, 73, 87, 97, 95, 91, 100, 118, 128

Offset

0,13

Comments

Number of partitions of n into distinct parts congruent to 3 or 4 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^A047204(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(17) = 3 because we have [14, 3], [13, 4] and [9, 8].

Mathematica

nmax = 74; CoefficientList[Series[Product[(1 + x^(5 k + 3)) (1 + x^(5 k + 4)), {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 74; CoefficientList[Series[QPochhammer[-x^3, x^5] QPochhammer[-x^4, x^5], {x, 0, nmax}], x]
nmax = 74; CoefficientList[Series[Product[(1 + Boole[MemberQ[{3, 4}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A035374, A047204, A107236, A107237, A203776, A219607, A281243, A281271, A301562, A301563, A301564, A301567, A301568, A301569, A301570.

Sequence in context: A344961 A343853 A143974 * A237265 A035463 A245424

Adjacent sequences: A301562 A301563 A301564 * A301566 A301567 A301568

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 23 2018

Status

approved