A161095 Number of partitions of n into squares where every part appears at least 7 times.

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, 2, 1, 1, 1, 2, 1, 1, 2, 3, 2, 2, 3, 4, 3, 3, 4, 5, 4, 4, 5, 6, 5, 5, 6, 7, 6, 6, 7, 8, 7, 7, 8, 9, 8, 8, 10, 10, 9, 9, 10, 11, 10, 11, 12, 14, 12, 12, 13, 14, 13, 13, 15, 16, 16, 15, 16, 17, 16, 16, 17, 19, 18, 19, 20, 20, 19, 19, 21, 21

Offset

1,28

Links

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

Formula

G.f.: Product_{k>=1} (1 + x^(7*k^2)/(1-x^(k^2))). - Vaclav Kotesovec, Jun 15 2025

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[(1 + x^(7*k^2)/(1-x^(k^2))), {k, 1, Sqrt[nmax]+1}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jun 15 2025 *)

Crossrefs

Sequence in context: A268057 A107435 A196056 * A276162 A118107 A236548

Adjacent sequences: A161092 A161093 A161094 * A161096 A161097 A161098

Keyword

nonn

Author

R. H. Hardin, Jun 02 2009

Status

approved