OFFSET
1,2
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,8,-8,-28,28,56,-56,-70,70,56,-56,-28,28,8,-8,-1,1).
FORMULA
a(n) = Sum_{i=1..floor(n/2)} i^7 + (n-i)^7.
From Colin Barker, Nov 20 2017: (Start)
G.f.: x^2*(2 + 127*x + 2299*x^2 + 15240*x^3 + 61848*x^4 + 151257*x^5 + 262139*x^6 + 306832*x^7 + 260914*x^8 + 151257*x^9 + 60777*x^10 + 15240*x^11 + 2180*x^12 + 127*x^13+ x^14) / ((1 - x)^9*(1 + x)^8).
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/2]}], {n, 40}]
PROG
(PARI) concat(0, Vec(x^2*(2 + 127*x + 2299*x^2 + 15240*x^3 + 61848*x^4 + 151257*x^5 + 262139*x^6 + 306832*x^7 + 260914*x^8 + 151257*x^9 + 60777*x^10 + 15240*x^11 + 2180*x^12 + 127*x^13+ x^14) / ((1 - x)^9*(1 + x)^8) + O(x^40))) \\ Colin Barker, Nov 20 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 26 2017
STATUS
approved