A161092 Number of partitions of n into squares where every part appears at least 4 times.

0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 2, 4, 3, 3, 3, 5, 4, 4, 4, 6, 5, 5, 5, 8, 6, 6, 6, 9, 8, 8, 8, 10, 10, 9, 9, 11, 11, 11, 11, 14, 12, 13, 12, 16, 14, 15, 15, 19, 18, 17, 18, 22, 21, 20, 21, 26, 26, 26, 25, 30, 29, 30, 29, 34, 34, 35, 35, 40, 39, 39, 40, 46, 46, 47, 48, 54

Offset

1,16

Links

R. H. Hardin, Table of n, a(n) for n=1..1000

Formula

G.f.: Product_{k>=1} (1 + x^(4*k^2)/(1-x^(k^2))). - Vaclav Kotesovec, Jun 15 2025

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[(1 + x^(4*k^2)/(1-x^(k^2))), {k, 1, Sqrt[nmax]+1}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jun 15 2025 *)

Crossrefs

Sequence in context: A292622 A292869 A106348 * A392670 A029332 A358172

Adjacent sequences: A161089 A161090 A161091 * A161093 A161094 A161095

Keyword

nonn

Author

R. H. Hardin, Jun 02 2009

Status

approved