A139579 a(n) = 2*n^2 + 15*n.

0, 17, 38, 63, 92, 125, 162, 203, 248, 297, 350, 407, 468, 533, 602, 675, 752, 833, 918, 1007, 1100, 1197, 1298, 1403, 1512, 1625, 1742, 1863, 1988, 2117, 2250, 2387, 2528, 2673, 2822, 2975, 3132, 3293, 3458, 3627, 3800, 3977, 4158, 4343, 4532, 4725, 4922, 5123, 5328, 5537

Offset

0,2

Links

Stefano Spezia, Table of n, a(n) for n = 0..10000

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

Formula

a(n) = a(n-1) + 4*n + 13; a(0) = 0. - Vincenzo Librandi, Nov 24 2010

From Stefano Spezia, Oct 21 2023: (Start)

O.g.f.: x*(17 - 13*x)/(1 - x)^3.

E.g.f.: exp(x)*x*(17 + 2*x). (End)

From Amiram Eldar, Nov 10 2023: (Start)

Sum_{n>=1} 1/a(n) = 182144/675675 - 2*log(2)/15.

Sum_{n>=1} (-1)^(n+1)/a(n) = log(2)/15 - Pi/30 + 67952/675675. (End)

Mathematica

LinearRecurrence[{3, -3, 1}, {0, 17, 38}, 50] (* Stefano Spezia, Oct 21 2023 *)

Prog

(PARI) a(n)=2*n^2+15*n \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A014105, A014106, A033537, A130861, A139576, A139577, A139578, A139580, A139581.

Sequence in context: A208292 A121710 A051779 * A293206 A125248 A259489

Adjacent sequences: A139576 A139577 A139578 * A139580 A139581 A139582

Keyword

easy,nonn

Author

Omar E. Pol, May 19 2008

Status

approved