A161090 Number of partitions of n into squares where every part appears at least 2 times.

0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 3, 5, 4, 6, 5, 6, 6, 7, 6, 8, 8, 9, 9, 11, 10, 13, 11, 14, 14, 16, 15, 18, 18, 20, 19, 22, 22, 25, 24, 27, 28, 32, 29, 36, 34, 39, 38, 42, 42, 47, 45, 51, 51, 56, 55, 62, 61, 68, 66, 75, 73, 82, 79, 88, 88, 96, 93, 104, 105, 112, 113, 122, 123

Offset

1,8

Links

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

Formula

G.f.: -1 + Product_{j>=1} (1 + x^(2j^2)/(1-x^(j^2))). - Emeric Deutsch, Jun 21 2009]

Example

a(12)=3 because we have 444, 441111, and 1^(12). - Emeric Deutsch, Jun 21 2009

Maple

g := -1+product(1+x^(2*j^2)/(1-x^(j^2)), j = 1 .. 10): gser := series(g, x = 0, 90): seq(coeff(gser, x, n), n = 1 .. 79); # Emeric Deutsch, Jun 21 2009

Crossrefs

Sequence in context: A059169 A026922 A178696 * A349219 A178697 A255065

Adjacent sequences: A161087 A161088 A161089 * A161091 A161092 A161093

Keyword

nonn

Author

R. H. Hardin, Jun 02 2009

Status

approved