A213424 Number of partitions of n in which all parts are >= 2 and the largest part occurs at least five times.

1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 3, 2, 3, 3, 5, 4, 6, 6, 8, 8, 12, 10, 15, 15, 19, 21, 26, 26, 34, 36, 45, 47, 59, 61, 76, 83, 97, 107, 128, 137, 165, 179, 210, 231, 271, 296, 345, 380, 438, 485, 561, 614, 708, 783, 893, 991, 1129, 1246, 1420, 1572, 1781

Offset

10,9

Links

Table of n, a(n) for n=10..70.

Formula

a(n) = A186445(n) - 2*A186445(n-1) + A186445(n-2).

G.f.: (1-x)*Product_{k>4} 1/(1-x^k)

Example

For n = 20 we have three partitions: {[4+4+4+4+4], [3+3+3+3+3+3+2], [2+2+2+2+2+2+2+2+2+2]}, so a(20) = 3.

Crossrefs

Cf. A000041, A186445, A213423.

Sequence in context: A364350 A053262 A007359 * A174427 A158206 A364062

Adjacent sequences: A213421 A213422 A213423 * A213425 A213426 A213427

Keyword

nonn

Author

Mircea Merca, Jun 11 2012

Status

approved