A301567 Expansion of Product_{k>=1} (1 + x^(5*k))*(1 + x^(5*k-4)).

1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 1, 3, 2, 0, 0, 2, 5, 4, 1, 0, 2, 7, 7, 2, 0, 3, 10, 11, 4, 0, 4, 14, 17, 8, 1, 5, 19, 25, 13, 2, 6, 25, 36, 21, 4, 8, 33, 50, 33, 8, 10, 43, 69, 49, 14, 13, 55, 93, 71, 23, 17, 70, 124, 102, 37, 22, 88, 163, 142, 57, 30, 110, 212, 195, 85

Offset

0,7

Comments

Number of partitions of n into distinct parts congruent to 0 or 1 mod 5.

Links

Table of n, a(n) for n=0..74.

Index entries for sequences related to partitions

Formula

G.f.: Product_{k>=2} (1 + x^A008851(k)).

a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(29/20) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Mar 24 2018

Example

a(11) = 3 because we have [11], [10, 1] and [6, 5].

Mathematica

nmax = 74; CoefficientList[Series[Product[(1 + x^(5 k)) (1 + x^(5 k - 4)), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 74; CoefficientList[Series[x^4 QPochhammer[-1, x^5] QPochhammer[-x^(-4), x^5]/(2 (1 + x^4)), {x, 0, nmax}], x]
nmax = 74; CoefficientList[Series[Product[(1 + Boole[MemberQ[{0, 1}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A008851, A035367, A036820, A203776, A219607, A280454, A301562, A301563, A301564, A301565, A301568, A301569, A301570.

Sequence in context: A319933 A335964 A301570 * A115363 A327191 A036867

Adjacent sequences: A301564 A301565 A301566 * A301568 A301569 A301570

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 23 2018

Status

approved