A274322 Number of partitions of n^2 into at most five parts.

1, 1, 5, 23, 101, 377, 1226, 3507, 9027, 21224, 46262, 94512, 182702, 336666, 595085, 1014091, 1673243, 2682685, 4192118, 6401314, 9572962, 14047457, 20260601, 28763703, 40247228, 55567352, 75776769, 102158957, 136267461, 179969238, 235493851, 305487369

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Formula

Coefficient of x^(n^2) in 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)).

a(n) = A001401(n^2).

Empirical g.f.: (1 -3*x +4*x^2 +13*x^3 +21*x^4 +63*x^5 +138*x^6 +204*x^7 +257*x^8 +280*x^9 +267*x^10 +201*x^11 +128*x^12 +67*x^13 +31*x^14 +6*x^15 +x^16 +x^17) / ((1 -x)^9*(1 +x)^3*(1 +x +x^2)*(1 +x +x^2 +x^3 +x^4)).

Prog

(PARI)
\\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)).
b(n) = round(((n+5)^4+10*((n+5)^3+(n+5)^2)-75*(n+5)-45*(n+5)*(-1)^(n+5))/2880)
vector(40, n, n--; b(n^2))

Crossrefs

A subsequence of A001401.

Sequence in context: A073682 A034958 A229008 * A085350 A113443 A124999

Adjacent sequences: A274319 A274320 A274321 * A274323 A274324 A274325

Keyword

nonn

Author

Colin Barker, Jun 20 2016

Status

approved