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A294288 Sum of the fourth powers of the parts in the partitions of n into two distinct parts. 7
0, 0, 17, 82, 354, 898, 2275, 4420, 8772, 14708, 25333, 38678, 60710, 86870, 127687, 174216, 243848, 320808, 432345, 552666, 722666, 902506, 1151403, 1410508, 1763020, 2125084, 2610621, 3103646, 3756718, 4413374, 5273999, 6131984, 7246096, 8348496, 9768353 (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 (1,5,-5,-10,10,10,-10,-5,5,1,-1).

FORMULA

a(n) = Sum_{i=1..floor((n-1)/2)} i^4 + (n-i)^4.

From Colin Barker, Nov 20 2017: (Start)

G.f.: x^3*(17 + 65*x + 187*x^2 + 219*x^3 + 187*x^4 + 75*x^5 + 17*x^6 + x^7) / ((1 - x)^6*(1 + x)^5).

a(n) = (1/480)*(n*(-16 + 160*n^2 - 15*(17 + (-1)^n)*n^3 + 96*n^4)).

a(n) = a(n-1) + 5*a(n-2) - 5*a(n-3) - 10*a(n-4) + 10*a(n-5) + 10*a(n-6) - 10*a(n-7) - 5*a(n-8) + 5*a(n-9) + a(n-10) - a(n-11) for n>11.

(End)

MATHEMATICA

Table[Sum[i^4 + (n - i)^4, {i, Floor[(n-1)/2]}], {n, 40}]

Rest@ CoefficientList[ Series[ x^3*(17 +65x +187x^2 +219x^3 +187x^4 +75x^5 +17x^6 +x^7)/((1 -x)^6*(1 +x)^5), {x, 0, 35}], x] (* or *)

LinearRecurrence[{1, 5, -5, -10, 10, 10, -10, -5, 5, 1, -1}, {0, 0, 17, 82, 354, 898, 2275, 4420, 8772, 14708, 25333}, 35] (* Robert G. Wilson v, Jan 07 2018 *)

PROG

(PARI) concat(vector(2), Vec(x^3*(17 + 65*x + 187*x^2 + 219*x^3 + 187*x^4 + 75*x^5 + 17*x^6 + x^7) / ((1 - x)^6*(1 + x)^5) + O(x^40))) \\ Colin Barker, Nov 20 2017

CROSSREFS

Sequence in context: A017671 A001159 A053820 * A296401 A259142 A142059

Adjacent sequences:  A294285 A294286 A294287 * A294289 A294290 A294291

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Oct 26 2017

STATUS

approved

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Last modified July 16 04:26 EDT 2019. Contains 325064 sequences. (Running on oeis4.)