A161254 Number of partitions of n into central polygonal numbers A000124.

1, 1, 2, 2, 4, 4, 6, 7, 10, 11, 14, 17, 21, 24, 29, 34, 41, 46, 55, 62, 73, 81, 96, 107, 124, 137, 158, 175, 199, 221, 250, 276, 310, 343, 383, 421, 469, 516, 572, 626, 693, 757, 833, 908, 1000, 1088, 1192, 1294, 1417, 1535, 1674, 1813, 1974, 2133, 2315, 2501, 2710, 2921

Offset

0,3

Links

R. H. Hardin, Table of n, a(n) for n = 0..1000

Formula

G.f.: 1 / (Product_{k>0} (1 - x^( (k^2 - k)/2 + 1))). - Michael Somos, May 29 2012

Example

1 + x + 2*x^2 + 2*x^3 + 4*x^4 + 4*x^5 + 6*x^6 + 7*x^7 + 10*x^8 + 11*x^9 + ...
a(4) = 4 since 4 = 2 + 2 = 2 + 1 + 1 = 1 + 1 + 1 + 1 is a partition in 4 ways. a(7) = 7 since 7 = 4 + 2 + 1 = 4 + 1 + 1 + 1 = 2 + 2 + 2 + 1 = 2 + 2 + 1 + 1 + 1 = 2 + 1 + 1 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1 + 1 is a partition in 7 ways. - Michael Somos, May 29 2012

Crossrefs

Cf. A000124.

Sequence in context: A029008 A240844 A136343 * A241313 A241317 A357456

Adjacent sequences: A161251 A161252 A161253 * A161255 A161256 A161257

Keyword

nonn

Author

R. H. Hardin, Jun 06 2009

Status

approved