A072243 Number of distinct partitions of n^2.

1, 1, 2, 8, 32, 142, 668, 3264, 16444, 84756, 444793, 2368800, 12769602, 69545358, 382075868, 2114965120, 11784471548, 66043042088, 372022512608, 2105220502772, 11962163400706, 68223286792200, 390406746862530, 2240962117491470, 12899456450932840

Offset: 0

Author

Robert G. Wilson v, Jul 06 2002

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1260 (terms 0..200 from Alois P. Heinz)

Crossrefs

Cf. A000009, A000041, A000290, A072213, A281489.

Programs

Maple

with(numtheory):
b:= proc(n) option remember; `if`(n=0, 1, add(add(
      `if`(d::odd, d, 0), d=divisors(j))*b(n-j), j=1..n)/n)
    end:
a:= n-> b(n^2):
seq(a(n), n=0..30);  # Alois P. Heinz, Jan 22 2017

Mathematica

Table[ PartitionsQ[n^2], {n, 1, 24}]

Formula

a(n) ~ exp(Pi*n/sqrt(3)) / (4*3^(1/4)*n^(3/2)). - Vaclav Kotesovec, Dec 01 2015

a(n) = A000009(A000290(n)). - Alois P. Heinz, Jan 22 2017

Extensions

a(0)=1 prepended by Alois P. Heinz, Jan 22 2017