A158408 a(n) = 900*n^2 - 2*n.

898, 3596, 8094, 14392, 22490, 32388, 44086, 57584, 72882, 89980, 108878, 129576, 152074, 176372, 202470, 230368, 260066, 291564, 324862, 359960, 396858, 435556, 476054, 518352, 562450, 608348, 656046, 705544, 756842, 809940, 864838, 921536

Offset

1,1

Comments

The identity (900*n - 1)^2 - (900*n^2 - 2*n)*30^2 = 1 can be written as A158409(n)^2 - a(n)*30^2 = 1.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(30^2*t-2)).

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

Formula

G.f.: 2*x*(449 + 451*x)/(1-x)^3. - Bruno Berselli, Dec 08 2011

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 12 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {898, 3596, 8094}, 50] (* Vincenzo Librandi, Feb 12 2012 *)

Prog

(Magma) I:=[898, 3596, 8094]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 12 2012
(PARI) for(n=1, 40, print1(900*n^2 - 2*n", ")); \\ Vincenzo Librandi, Feb 12 2012

Crossrefs

Cf. A158409.

Sequence in context: A145498 A252378 A210129 * A158409 A061044 A344595

Adjacent sequences: A158405 A158406 A158407 * A158409 A158410 A158411

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved