A161294 Number of partitions of n into numbers not divisible by 4 where every part appears at least 3 times.

0, 0, 1, 1, 1, 2, 1, 2, 3, 3, 3, 6, 5, 6, 10, 8, 9, 15, 13, 16, 22, 20, 24, 33, 32, 36, 47, 48, 53, 71, 68, 77, 100, 99, 112, 140, 138, 158, 194, 199, 219, 268, 275, 305, 369, 377, 416, 501, 514, 572, 671, 693, 768, 898, 935, 1028, 1189, 1245, 1364, 1576, 1642, 1798, 2063

Offset

1,6

Links

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

Formula

G.f.: -1 + (Product_{j>=1} (1 + x^(3*j)/(1-x^j)))/Product_{j>=1} (1 + x^(12*j)/(1-x^(4*j))). - Emeric Deutsch, Jun 21 2009

Example

a(13)=5 because we have (3^3)(1^4), (2^5)(1^3), (2^4)(1^5), (2^3)(1^7), and 1^(13). - Emeric Deutsch, Jun 21 2009

Maple

g := -1+(product(1+x^(3*j)/(1-x^j), j = 1 .. 40))/(product(1+x^(12*j)/(1-x^(4*j)), j = 1 .. 40)): gser := series(g, x = 0, 70): seq(coeff(gser, x, n), n = 2 .. 68); # Emeric Deutsch, Jun 21 2009

Crossrefs

Sequence in context: A161242 A161027 A161078 * A161269 A100405 A081366

Adjacent sequences: A161291 A161292 A161293 * A161295 A161296 A161297

Keyword

nonn

Author

R. H. Hardin, Jun 06 2009

Status

approved