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

Author

Vladimir Joseph Stephan Orlovsky, Dec 05 2008

Keywords

• nonn
• easy

Comments

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

Links

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

Programs

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 *)

PARI

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

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

Extensions

Definition corrected by Jeremy Gardiner, Jun 15 2013