A161091 Number of partitions of n into squares where every part appears at least 3 times.

0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 2, 2, 3, 4, 3, 3, 4, 5, 4, 4, 6, 6, 5, 6, 7, 8, 7, 7, 8, 10, 8, 8, 11, 11, 10, 11, 13, 13, 13, 13, 15, 18, 15, 16, 20, 21, 19, 21, 23, 24, 24, 24, 27, 30, 28, 28, 33, 36, 33, 35, 39, 42, 41, 42, 45, 49, 47, 48, 55, 56, 54, 58, 63, 67, 65, 66, 72, 78

Offset

1,12

Links

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

Formula

G.f.: Product_{j>=1} (1 + x^(3j^2)/(1-x^(j^2))). - Emeric Deutsch, Jun 24 2009

Example

a(23)=4 because we have (4^5)(1^3), (4^4)(1^7), (4^3)(1^11), and (1^23). - Emeric Deutsch, Jun 24 2009

Maple

g := product(1+x^(3*j^2)/(1-x^(j^2)), j = 1 .. 20): gser := series(g, x = 0, 90): seq(coeff(gser, x, n), n = 2 .. 84); # Emeric Deutsch, Jun 24 2009

Crossrefs

Sequence in context: A334591 A177962 A246552 * A027347 A352131 A035438

Adjacent sequences: A161088 A161089 A161090 * A161092 A161093 A161094

Keyword

nonn

Author

R. H. Hardin, Jun 02 2009

Status

approved