A206808 Sum_{0

7, 45, 156, 400, 855, 1617, 2800, 4536, 6975, 10285, 14652, 20280, 27391, 36225, 47040, 60112, 75735, 94221, 115900, 141120, 170247, 203665, 241776, 285000, 333775, 388557, 449820, 518056, 593775, 677505, 769792, 871200, 982311

Offset: 2

Author

Clark Kimberling, Feb 15 2012

Keywords

• nonn
• easy

Comments

a(n) = n^4-p(n), where p(n) is the n-th partial sum of (j^3).

a(n) = t(n)-t(n-1), where t = A206809.

For a guide to related sequences, see A206817.

Examples

			a(2) = 2^3-1^3 = 7.
a(3) = (3^3-1^3) + (3^3-2^3) = 45.
		

Links

• Danny Rorabaugh, Table of n, a(n) for n = 2..10000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A206817, A206806.

Programs

Mathematica

s[k_] := k^3; 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}]  (* A206808 *)
Flatten[Table[t[n], {n, 2, 35}]]  (* A206809 *)

PARI

vector(100, n, (3*n^4+10*n^3+11*n^2+4*n)/4) \\ Colin Barker, Jul 11 2014

PARI

Vec(-x^2*(x^2+10*x+7)/(x-1)^5 + O(x^100)) \\ Colin Barker, Jul 11 2014

Sage

[sum([n^3-j^3 for j in range(1,n)]) for n in range(2,35)] # Danny Rorabaugh, Apr 18 2015

Formula

a(n) = (3*n^4-2*n^3-n^2)/4. G.f.: -x^2*(x^2+10*x+7) / (x-1)^5. - Colin Barker, Jul 11 2014