A301570 Expansion of Product_{k>=1} (1 + x^(5*k))*(1 + x^(5*k-1)).

1, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 0, 0, 1, 3, 2, 0, 0, 2, 5, 2, 0, 0, 4, 7, 3, 0, 1, 7, 10, 4, 0, 2, 11, 14, 5, 0, 4, 17, 19, 6, 0, 8, 25, 25, 8, 1, 13, 36, 33, 10, 2, 21, 50, 43, 12, 4, 33, 69, 55, 15, 8, 49, 93, 70, 18, 14, 71, 124, 88, 23, 23, 102, 163, 110, 29, 37

Offset

0,10

Comments

Number of partitions of n into distinct parts congruent to 0 or 4 mod 5.

Links

Table of n, a(n) for n=0..76.

Index entries for sequences related to partitions

Formula

G.f.: Product_{k>=2} (1 + x^A047208(k)).

a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(41/20) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Mar 24 2018

Example

a(14) = 3 because we have [14], [10, 4] and [9, 5].

Mathematica

nmax = 76; CoefficientList[Series[Product[(1 + x^(5 k)) (1 + x^(5 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 76; CoefficientList[Series[x QPochhammer[-1, x^5] QPochhammer[-x^(-1), x^5]/(2 (1 + x)), {x, 0, nmax}], x]
nmax = 76; CoefficientList[Series[Product[(1 + Boole[MemberQ[{0, 4}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A035370, A036820, A047208, A203776, A219607, A281243, A301562, A301563, A301564, A301565, A301567, A301568, A301569.

Sequence in context: A071676 A319933 A335964 * A301567 A115363 A327191

Adjacent sequences: A301567 A301568 A301569 * A301571 A301572 A301573

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 23 2018

Status

approved