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A262925 Sum of n consecutive fourth powers starting with n^4. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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).

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.

EXAMPLE

a(3) = 3^4 + 4^4 + 5^4 = 962.

MATHEMATICA

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 1, 97, 962, 4578, 14979}, 30] (* Harvey P. Dale, Jul 30 2017 *)

PROG

(PARI) vector(40, n, n--; sum(k=n, 2*n-1, k^4))

(PARI) concat(0, Vec(x*(16*x^4+241*x^3+395*x^2+91*x+1)/(x-1)^6 + O(x^40)))

CROSSREFS

Cf. A050410, A240137, A262926.

Sequence in context: A090157 A162674 A070845 * A093297 A068852 A093944

Adjacent sequences:  A262922 A262923 A262924 * A262926 A262927 A262928

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Oct 04 2015

STATUS

approved

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Last modified September 26 22:11 EDT 2022. Contains 357051 sequences. (Running on oeis4.)