A139578 a(n) = n*(2*n + 13).

0, 15, 34, 57, 84, 115, 150, 189, 232, 279, 330, 385, 444, 507, 574, 645, 720, 799, 882, 969, 1060, 1155, 1254, 1357, 1464, 1575, 1690, 1809, 1932, 2059, 2190, 2325, 2464, 2607, 2754, 2905, 3060, 3219, 3382, 3549, 3720, 3895, 4074, 4257, 4444, 4635, 4830, 5029

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 2*n^2 + 13*n.

a(n) = a(n-1) + 4*n + 11 (with a(0)=0). - Vincenzo Librandi, Nov 24 2010

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

G.f.: x*(15 - 11*x)/(1 - x)^3.

E.g.f.: exp(x)*x*(15 + 2*x).

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

Mathematica

s=0; lst={s}; Do[s+=n++ +15; AppendTo[lst, s], {n, 0, 7!, 4}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 19 2008 *)
Table[n(2n+13), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 15, 34}, 50] (* Harvey P. Dale, Nov 22 2014 *)

Prog

(PARI) a(n)=n*(2*n+13) \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A014105, A014106, A033537, A130861, A139576, A139577, A139579, A139580, A139581.

Sequence in context: A270072 A085803 A168573 * A345733 A297729 A156662

Adjacent sequences: A139575 A139576 A139577 * A139579 A139580 A139581

Keyword

easy,nonn

Author

Omar E. Pol, May 19 2008

Status

approved