A147785 Number of partitions of n into parts divisible by 3 or 5.

1, 0, 0, 1, 0, 1, 2, 0, 1, 3, 2, 2, 5, 2, 3, 9, 4, 5, 13, 6, 11, 19, 10, 15, 28, 19, 23, 40, 27, 34, 63, 40, 50, 85, 59, 79, 121, 85, 109, 166, 132, 155, 230, 180, 216, 325, 255, 300, 436, 351, 429, 588, 485, 576, 789, 680, 784, 1050, 912, 1053, 1421, 1228

Offset

0,7

Comments

Also number of partitions of n with no part and no difference between two parts equal to 1,2,4 or 7.

Also number of partitions of n with no part appearing 1,2,4 or 7 times.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

A. E. Holroyd, Partition Identities and the Coin Exchange Problem, arXiv:0706.2282 [math.CO], 2007.

A. E. Holroyd, Partition Identities and the Coin Exchange Problem, J. Combin. Theory Ser. A, 115 (2008) 1096-1101.

Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 17.

Formula

G.f.: Product_{k>=1} (1-x^(15k)) / ((1-x^(3k))*(1-x^(5k))).

a(n) ~ sqrt(7/5) * exp(sqrt(14*n/5)*Pi/3) / (12*n). - Vaclav Kotesovec, Sep 23 2015

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(
      `if`(irem(d, 3)=0 or irem(d, 5)=0, d, 0),
           d=divisors(j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..65);  # Alois P. Heinz, Dec 02 2016

Mathematica

nmax = 60; CoefficientList[Series[Product[(1-x^(15*k))/((1-x^(3*k))*(1-x^(5*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 23 2015 *)

Crossrefs

Cf. A007690, A147783, A147784, A147786, A147787.

Sequence in context: A022827 A302764 A091889 * A067591 A097609 A266692

Adjacent sequences: A147782 A147783 A147784 * A147786 A147787 A147788

Keyword

nonn

Author

Alexander E. Holroyd (holroyd at math.ubc.ca)

Status

approved