A158406 a(n) = 900*n^2 + 2*n.

902, 3604, 8106, 14408, 22510, 32412, 44114, 57616, 72918, 90020, 108922, 129624, 152126, 176428, 202530, 230432, 260134, 291636, 324938, 360040, 396942, 435644, 476146, 518448, 562550, 608452, 656154, 705656, 756958, 810060, 864962, 921664

Offset

1,1

Comments

The identity (900*n + 1)^2 - (900*n^2 + 2*n)*30^2 = 1 can be written as A158407(n)^2 - a(n)*30^2 = 1. - Vincenzo Librandi, Feb 09 2012

Links

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

Vincenzo Librandi, X^2-AY^2=1

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

Formula

G.f.: x*(-902 - 898*x)/(x-1)^3. - Vincenzo Librandi, Feb 09 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 09 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {902, 3604, 8106}, 50] (* Vincenzo Librandi, Feb 09 2012 *)

Prog

(Magma) I:=[902, 3604, 8106]; [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 09 2012
(PARI) for(n=1, 40, print1(900*n^2 + 2*n", ")); \\ Vincenzo Librandi, Feb 09 2012

Crossrefs

Cf. A158407.

Sequence in context: A345537 A345789 A031528 * A323143 A284744 A111042

Adjacent sequences: A158403 A158404 A158405 * A158407 A158408 A158409

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved