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A274252
Number of partitions of n^5 into at most three parts.
5
1, 1, 102, 5043, 87894, 815365, 5042737, 23548008, 89494870, 290594892, 833383334, 2161532576, 5159904769, 11488393301, 24104823494, 48054578907, 91626493270, 168000201633, 297539880337, 510923426200, 853334933334, 1389992123568, 2213329476102, 3452212485976
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (9, -35, 76, -99, 77, -33, 0, 33, -77, 99, -76, 35, -9, 1).
FORMULA
Coefficient of x^(n^5) in 1/((1-x)*(1-x^2)*(1-x^3)).
G.f.: (1 -8*x +128*x^2 +4084*x^3 +46100*x^4 +193094*x^5 +407528*x^6 +512642*x^7 +407381*x^8 +193090*x^9 +46120*x^10 +4170*x^11 +70*x^12) / ((1 -x)^11*(1 +x)*(1 +x +x^2)).
a(n) = A001399(n^5) = round((n^5+3)^2/12). - Alois P. Heinz, Jun 16 2016
MATHEMATICA
CoefficientList[Series[(1-8x+128x^2+4084x^3+46100x^4+193094x^5+407528x^6+512642x^7+407381x^8+193090x^9+46120x^10+4170x^11+70x^12)/((1-x)^11(1+x)(1+x+x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{9, -35, 76, -99, 77, -33, 0, 33, -77, 99, -76, 35, -9, 1}, {1, 1, 102, 5043, 87894, 815365, 5042737, 23548008, 89494870, 290594892, 833383334, 2161532576, 5159904769, 11488393301}, 30] (* Harvey P. Dale, May 15 2023 *)
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^5))
CROSSREFS
A subsequence of A001399.
Cf. A274250 (n^2), A274251 (n^3), A274253 (n^7), A274254 (n^11).
Sequence in context: A203401 A217331 A284448 * A303993 A030512 A097725
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jun 16 2016
STATUS
approved