A262925 Sum of n consecutive fourth powers starting with n^4.
0, 1, 97, 962, 4578, 14979, 38995, 86996, 173636, 318597, 547333, 891814, 1391270, 2092935, 3052791, 4336312, 6019208, 8188169, 10941609, 14390410, 18658666, 23884427, 30220443, 37834908, 46912204, 57653645, 70278221, 85023342, 102145582, 121921423
Offset: 0
Examples
a(3) = 3^4 + 4^4 + 5^4 = 962.
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Programs
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Mathematica
LinearRecurrence[{6,-15,20,-15,6,-1},{0,1,97,962,4578,14979},30] (* Harvey P. Dale, Jul 30 2017 *) -
PARI
vector(40, n, n--; sum(k=n, 2*n-1, k^4))
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PARI
concat(0, Vec(x*(16*x^4+241*x^3+395*x^2+91*x+1)/(x-1)^6 + O(x^40)))
Formula
a(n) = n*(-1+70*n^2-225*n^3+186*n^4)/30.
G.f.: x*(16*x^4+241*x^3+395*x^2+91*x+1) / (x-1)^6.