A161102 Number of partitions of n into squares where every part appears at least 14 times.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 6, 7, 7, 8, 7, 8, 8, 9, 8, 9, 9, 10, 9, 10, 10, 11, 10, 11, 11, 12, 11, 12, 12, 13, 12

Offset

1,56

Links

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

Formula

G.f.: Product_{k>=1} (1 + x^(14*k^2)/(1-x^(k^2))). - Vaclav Kotesovec, Jun 15 2025

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[(1 + x^(14*k^2)/(1-x^(k^2))), {k, 1, Sqrt[nmax]+1}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jun 15 2025 *)

Crossrefs

Sequence in context: A333748 A022929 A307706 * A276329 A161101 A115362

Adjacent sequences: A161099 A161100 A161101 * A161103 A161104 A161105

Keyword

nonn

Author

R. H. Hardin, Jun 02 2009

Status

approved