A161097 Number of partitions of n into squares where every part appears at least 9 times.

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, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 12, 11, 11, 12, 12, 12, 12, 13, 13, 15, 14, 15, 15, 15, 15, 16, 16, 16, 18, 18, 18

Offset

1,36

Links

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

Formula

G.f.: Product_{k>=1} (1 + x^(9*k^2)/(1-x^(k^2))). - Vaclav Kotesovec, Jun 15 2025

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[(1 + x^(9*k^2)/(1-x^(k^2))), {k, 1, Sqrt[nmax]+1}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jun 15 2025 *)

Crossrefs

Sequence in context: A033183 A351742 A090677 * A105240 A327499 A353693

Adjacent sequences: A161094 A161095 A161096 * A161098 A161099 A161100

Keyword

nonn

Author

R. H. Hardin, Jun 02 2009

Status

approved