A274250 Number of partitions of n^2 into at most three parts.

1, 1, 4, 12, 30, 65, 127, 225, 374, 588, 884, 1281, 1801, 2465, 3300, 4332, 5590, 7105, 8911, 11041, 13534, 16428, 19764, 23585, 27937, 32865, 38420, 44652, 51614, 59361, 67951, 77441, 87894, 99372, 111940, 125665, 140617, 156865, 174484, 193548, 214134

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,0,1,2,-3,1).

Formula

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

G.f.: (1-2*x+3*x^2+3*x^3+3*x^4+2*x^5+x^6+x^7) / ((1-x)^5*(1+x)*(1+x+x^2)).

a(n) = A001399(n^2) = round((n^2+3)^2/12). - Alois P. Heinz, Jun 16 2016

Prog

(PARI)
\\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)*(1-x^3)).
b(n) = round(real((47+9*(-1)^n + 8*exp(-2/3*I*n*Pi) + 8*exp((2*I*n*Pi)/3) + 36*n+6*n^2)/72))
vector(50, n, n--; b(n^2))

Crossrefs

A subsequence of A001399.

Cf. A274251 (n^3), A274252 (n^5), A274253 (n^7), A274254 (n^11).

Sequence in context: A367097 A212519 A166213 * A004036 A011797 A051172

Adjacent sequences: A274247 A274248 A274249 * A274251 A274252 A274253

Keyword

nonn,easy

Author

Colin Barker, Jun 16 2016

Status

approved