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A206810 Sum_{0<j<n} (n^4-j^4). 3
15, 145, 670, 2146, 5501, 12131, 23996, 43716, 74667, 121077, 188122, 282022, 410137, 581063, 804728, 1092488, 1457223, 1913433, 2477334, 3166954, 4002229, 5005099, 6199604, 7611980, 9270755, 11206845, 13453650, 16047150 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

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 (6,-15,20,-15,6,-1).

FORMULA

a(n) = n^5-p(n), where p(n) is the n-th partial sum of (j^4).

a(n) = t(n)-t(n-1), where t = A206811.

a(n) = (n-10*n^3-15*n^4+24*n^5)/30. G.f.: x^2*(x^3+25*x^2+55*x+15) / (x-1)^6. - Colin Barker, Jul 11 2014

EXAMPLE

a(2) = 2^4-1^4 = 15.

a(3) = (3^4-1^4) + (3^4-2^4) = 145.

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)^6 + O(x^100)) \\ Colin Barker, Jul 11 2014

(Sage) [sum([n^4-j^4 for j in range(1, n)]) for n in range(2, 30)] # Danny Rorabaugh, Apr 18 2015

CROSSREFS

Cf. A206817, A206811.

Sequence in context: A270511 A026893 A163799 * A025440 A155638 A252982

Adjacent sequences:  A206807 A206808 A206809 * A206811 A206812 A206813

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 15 2012

STATUS

approved

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Last modified January 20 14:26 EST 2020. Contains 331094 sequences. (Running on oeis4.)