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A294302 Sum of the seventh powers of the parts in the partitions of n into two distinct parts. 4
0, 0, 129, 2188, 18700, 94638, 376761, 1183920, 3297456, 8002300, 18080425, 37287660, 73399404, 135324378, 241561425, 410323648, 680856256, 1086411960, 1703414961, 2587286700, 3877286700, 5658888070, 8172733129, 11541726768, 16164030000, 22204797108 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for sequences related to partitions

Index entries for linear recurrences with constant coefficients, signature (1,8,-8,-28,28,56,-56,-70,70,56,-56,-28,28,8,-8,-1,1).

FORMULA

a(n) = Sum_{i=1..floor((n-1)/2)} i^7 + (n-i)^7.

From Colin Barker, Nov 20 2017: (Start)

G.f.: x^3*(129 + 2059*x + 15480*x^2 + 59466*x^3 + 153639*x^4 + 257307*x^5 + 311664*x^6 + 258532*x^7 + 153639*x^8 + 60537*x^9 + 15480*x^10 + 2178*x^11 + 129*x^12 + x^13) / ((1 - x)^9*(1 + x)^8).

a(n) = (1/768)*(n^2*(64 - 224*n^2 + 448*n^4 - 3*(129 + (-1)^n)*n^5 + 96*n^6)).

a(n) = a(n-1) + 8*a(n-2) - 8*a(n-3) - 28*a(n-4) + 28*a(n-5) + 56*a(n-6) - 56*a(n-7) - 70*a(n-8) + 70*a(n-9) + 56*a(n-10) - 56*a(n-11) - 28*a(n-12) + 28*a(n-13) + 8*a(n-14) - 8*a(n-15) - a(n-16) + a(n-17) for n>17.

(End)

MATHEMATICA

Table[Sum[i^7 + (n - i)^7, {i, Floor[(n-1)/2]}], {n, 40}]

PROG

(PARI) a(n) = sum(i=1, (n-1)\2, i^7 + (n-i)^7); \\ Michel Marcus, Nov 08 2017

(PARI) concat(vector(2), Vec(x^3*(129 + 2059*x + 15480*x^2 + 59466*x^3 + 153639*x^4 + 257307*x^5 + 311664*x^6 + 258532*x^7 + 153639*x^8 + 60537*x^9 + 15480*x^10 + 2178*x^11 + 129*x^12 + x^13) / ((1 - x)^9*(1 + x)^8) + O(x^40))) \\ Colin Barker, Nov 20 2017

CROSSREFS

Cf. A294286, A294287, A294288, A294300, A294301.

Sequence in context: A034681 A017677 A013955 * A221969 A036085 A000541

Adjacent sequences:  A294299 A294300 A294301 * A294303 A294304 A294305

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Oct 27 2017

STATUS

approved

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Last modified January 17 22:39 EST 2019. Contains 319251 sequences. (Running on oeis4.)