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 A294271 Sum of the fourth powers of the parts in the partitions of n into two parts. 1
 0, 2, 17, 114, 354, 1060, 2275, 4932, 8772, 15958, 25333, 41270, 60710, 91672, 127687, 182408, 243848, 333930, 432345, 572666, 722666, 931788, 1151403, 1451980, 1763020, 2182206, 2610621, 3180478, 3756718, 4514624, 5273999, 6263056, 7246096, 8515538, 9768353 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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/2)} i^4 + (n-i)^4. From Colin Barker, Nov 20 2017: (Start) G.f.: x^2*(2 + 15*x + 87*x^2 + 165*x^3 + 241*x^4 + 165*x^5 + 77*x^6 + 15*x^7 + x^8) / ((1 - x)^6*(1 + x)^5). a(n) = (1/480)*(n*(-16 + 160*n^2 + 15*(-15 + (-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/2]}], {n, 60}] Table[Total[Flatten[IntegerPartitions[n, {2}]]^4], {n, 40}] (* Harvey P. Dale, Mar 01 2019 *) PROG (PARI) concat(0, Vec(x^2*(2 + 15*x + 87*x^2 + 165*x^3 + 241*x^4 + 165*x^5 + 77*x^6 + 15*x^7 + x^8) / ((1 - x)^6*(1 + x)^5) + O(x^40))) \\ Colin Barker, Nov 20 2017 (PARI) a(n) = sum(i=1, n\2, i^4 + (n-i)^4); \\ Michel Marcus, Nov 20 2017 CROSSREFS Sequence in context: A213785 A198158 A203247 * A203123 A198043 A037747 Adjacent sequences: A294268 A294269 A294270 * A294272 A294273 A294274 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Oct 26 2017 STATUS approved

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Last modified June 17 09:14 EDT 2024. Contains 373444 sequences. (Running on oeis4.)