A274253 Number of partitions of n^7 into at most three parts.

1, 1, 1430, 399675, 22377814, 508665365, 6530486977, 56519001176, 366504924502, 1906401762732, 8333338333334, 31645829208856, 106993223294977, 328114730182533, 926000621503254, 2432743920878907, 6004799637378390, 14031485751786081, 31234447604616769

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (13, -77, 274, -650, 1078, -1274, 1066, -572, 0, 572, -1066, 1274, -1078, 650, -274, 77, -13, 1).

Formula

Coefficient of x^(n^7) in 1/((1-x)*(1-x^2)*(1-x^3)).

G.f.: (1 -12*x +1494*x^2 +380888*x^3 +17292525*x^4 +248136510*x^5 +1532347656*x^6 +4916629962*x^7 +9347647209*x^8 +11464268960*x^9 +9347652702*x^10 +4916635404*x^11 +1532337619*x^12 +248138478*x^13 +17294340*x^14 +380562*x^15 +1302*x^16) / ((1 -x)^15*(1 +x)*(1 +x +x^2)).

a(n) = A001399(n^7) = round((n^7+3)^2/12). - Alois P. Heinz, Jun 16 2016

Mathematica

CoefficientList[Series[(1-12x+1494x^2+380888x^3+17292525x^4+248136510x^5+1532347656x^6+ 4916629962x^7+ 9347647209x^8+11464268960x^9+9347652702x^10+ 4916635404x^11+ 1532337619x^12+ 248138478x^13+17294340x^14+380562x^15+1302x^16)/((1-x)^15(1+x)(1+x+x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{13, -77, 274, -650, 1078, -1274, 1066, -572, 0, 572, -1066, 1274, -1078, 650, -274, 77, -13, 1}, {1, 1, 1430, 399675, 22377814, 508665365, 6530486977, 56519001176, 366504924502, 1906401762732, 8333338333334, 31645829208856, 106993223294977, 328114730182533, 926000621503254, 2432743920878907, 6004799637378390, 14031485751786081}, 30] (* Harvey P. Dale, Dec 09 2022 *)

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^7))

Crossrefs

A subsequence of A001399.

Cf. A274250 (n^2), A274251 (n^3), A274252 (n^5), A274254 (n^11).

Sequence in context: A258495 A258396 A215548 * A227598 A321977 A147695

Adjacent sequences: A274250 A274251 A274252 * A274254 A274255 A274256

Keyword

nonn,easy

Author

Colin Barker, Jun 16 2016

Status

approved