A139576 a(n) = n*(2*n + 9).

0, 11, 26, 45, 68, 95, 126, 161, 200, 243, 290, 341, 396, 455, 518, 585, 656, 731, 810, 893, 980, 1071, 1166, 1265, 1368, 1475, 1586, 1701, 1820, 1943, 2070, 2201, 2336, 2475, 2618, 2765, 2916, 3071, 3230, 3393, 3560, 3731, 3906

Offset: 0

Author

Omar E. Pol, May 19 2008

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A014105, A014106, A033537, A130861, A139577, A139578, A139579, A139580, A139581.

Cf. A277979.

Programs

Mathematica

s=0;lst={s};Do[s+=n++ +11;AppendTo[lst, s], {n, 0, 7!, 4}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 19 2008 *)
Table[Sum[(2*i + n - 1), {i, 4, n}], {n, 3, 45}] (* Zerinvary Lajos, Jul 11 2009 *)
Table[n(2n+9),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,11,26},50] (* Harvey P. Dale, Dec 18 2018 *)

PARI

a(n)=n*(2*n+9) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 2*n^2 + 9*n.

a(n) = a(n-1) + 4*n + 7 (with a(0)=0). - Vincenzo Librandi, Nov 24 2010

From Elmo R. Oliveira, Nov 29 2024: (Start)

G.f.: x*(11 - 7*x)/(1-x)^3.

E.g.f.: exp(x)*x*(11 + 2*x).

a(n) = A277979(n)/2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)