OFFSET
1,2
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 26 2017
STATUS
approved