A206811 Sum_{0<j<k<=n} (k^4-j^4).

15, 160, 830, 2976, 8477, 20608, 44604, 88320, 162987, 284064, 472186, 754208, 1164345, 1745408, 2550136, 3642624, 5099847, 7013280, 9490614, 12657568, 16659797, 21664896, 27864500, 35476480, 44747235, 55954080, 69407730

Offset

2,1

Comments

Partial sums of A206810. For a guide to related sequences, see A206817.

Links

Danny Rorabaugh, Table of n, a(n) for n = 2..10000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = (n*(1+n)^2*(1-6*n+n^2+4*n^3))/30. G.f.: -x^2*(x^3+25*x^2+55*x+15) / (x-1)^7. - Colin Barker, Jul 11 2014

Example

a(4) = 16-1 + 81-1 + 81-16 = 160.

Mathematica

s[k_] := k^4; t[1] = 0;
p[n_] := Sum[s[k], {k, 1, n}];
c[n_] := n*s[n] - p[n];
t[n_] := t[n - 1] + (n - 1) s[n] - p[n - 1]
Table[c[n], {n, 2, 50}]  (* A206810  *)
Flatten[Table[t[n], {n, 2, 35}]] (* A206811 *)

Prog

(PARI) Vec(-x^2*(x^3+25*x^2+55*x+15)/(x-1)^7 + O(x^100)) \\ Colin Barker, Jul 11 2014
(Sage) [sum([sum([k^4-j^4 for j in range(1, k)]) for k in range(2, n+1)]) for n in range(2, 29)] # Danny Rorabaugh, Apr 18 2015

Crossrefs

Cf. A206810, A206817.

Sequence in context: A183555 A232415 A016297 * A027544 A021048 A095685

Adjacent sequences: A206808 A206809 A206810 * A206812 A206813 A206814

Keyword

nonn,easy

Author

Clark Kimberling, Feb 15 2012

Status

approved