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A274251 Number of partitions of n^3 into at most three parts. 5
1, 1, 10, 75, 374, 1365, 3997, 9976, 22102, 44652, 83834, 148296, 249697, 403333, 628834, 950907, 1400150, 2013921, 2837269, 3923920, 5337334, 7151808, 9453650, 12342408, 15932161, 20352865, 25751770, 32294883, 40168502, 49580805, 60763501, 73973536 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
Coefficient of x^(n^3) in 1/((1-x)*(1-x^2)*(1-x^3)).
G.f. (1-4*x+14*x^2+28*x^3+83*x^4+110*x^5+88*x^6+38*x^7+2*x^8) / ((1-x)^7*(1+x)*(1+x+x^2)).
a(n) = A001399(n^3) = round((n^3+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^3))
CROSSREFS
A subsequence of A001399.
Cf. A274250 (n^2), A274252 (n^5), A274253 (n^7), A274254 (n^11).
Sequence in context: A027778 A026969 A026979 * A073379 A283238 A316462
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jun 16 2016
STATUS
approved

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Last modified July 21 02:16 EDT 2024. Contains 374462 sequences. (Running on oeis4.)