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A274250 Number of partitions of n^2 into at most three parts. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jun 16 2016
STATUS
approved

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Last modified July 25 04:49 EDT 2024. Contains 374586 sequences. (Running on oeis4.)