A301562 Expansion of Product_{k>=0} (1 + x^(5*k+1))*(1 + x^(5*k+2)).

1, 1, 1, 1, 0, 0, 1, 2, 2, 2, 1, 1, 2, 3, 3, 2, 2, 3, 5, 6, 5, 4, 4, 6, 8, 8, 7, 7, 9, 12, 13, 11, 10, 12, 16, 19, 19, 17, 18, 23, 27, 27, 25, 25, 30, 37, 40, 38, 37, 42, 50, 55, 54, 52, 57, 68, 77, 78, 75, 78, 90, 102, 106, 104, 106, 120, 138, 146, 144, 145, 158

Offset

0,8

Comments

Number of partitions of n into distinct parts congruent to 1 or 2 mod 5.

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^A047216(k)).

a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(17/20) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Mar 24 2018

Example

a(13) = 3 because we have [12, 1], [11, 2] and [7, 6].

Mathematica

nmax = 70; CoefficientList[Series[Product[(1 + x^(5 k + 1)) (1 + x^(5 k + 2)), {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 70; CoefficientList[Series[QPochhammer[-x, x^5] QPochhammer[-x^2, x^5], {x, 0, nmax}], x]
nmax = 70; CoefficientList[Series[Product[(1 + Boole[MemberQ[{1, 2}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A035371, A047216, A107234, A107235, A203776, A219607, A280454, A281272, A301563, A301564, A301565, A301567, A301568, A301569, A301570.

Sequence in context: A085684 A141604 A143996 * A334486 A356997 A171412

Adjacent sequences: A301559 A301560 A301561 * A301563 A301564 A301565

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 23 2018

Status

approved