A152457 Partial sums of A027444.

0, 3, 17, 56, 140, 295, 553, 952, 1536, 2355, 3465, 4928, 6812, 9191, 12145, 15760, 20128, 25347, 31521, 38760, 47180, 56903, 68057, 80776, 95200, 111475, 129753, 150192, 172956, 198215, 226145, 256928, 290752, 327811, 368305, 412440, 460428

Offset

0,2

Comments

1^1+1^2+1^3=3; (2^1+2^2+2^3)+3=17; ...

Links

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Formula

a(n) = n(n + 1)(3n^2 + 7n + 8)/12. - Giovanni Resta, Jun 15 2013

a(0)=0, a(1)=3, a(2)=17, a(3)=56, a(4)=140, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5). - Harvey P. Dale, Dec 13 2013

G.f.: -x*(3+2*x+x^2) / (x-1)^5 . - R. J. Mathar, Jul 18 2016

Mathematica

Table[Sum[i + i^2 + i^3, {i, n}], {n, 0, 25}]
Accumulate[Table[n^3+n^2+n, {n, 0, 50}]] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {0, 3, 17, 56, 140}, 50] (* Harvey P. Dale, Dec 13 2013 *)

Prog

(PARI) a(n)=n*(n+1)*(3*n^2+7*n+8)/12 \\ Charles R Greathouse IV, Oct 21 2022

Crossrefs

Sequence in context: A361525 A033562 A212415 * A130857 A226719 A168547

Adjacent sequences: A152454 A152455 A152456 * A152458 A152459 A152460

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Dec 05 2008

Extensions

Definition corrected by Jeremy Gardiner, Jun 15 2013

Status

approved