A158305 - OEIS

A158305

324n^2 - 2n.

322, 1292, 2910, 5176, 8090, 11652, 15862, 20720, 26226, 32380, 39182, 46632, 54730, 63476, 72870, 82912, 93602, 104940, 116926, 129560, 142842, 156772, 171350, 186576, 202450, 218972, 236142, 253960, 272426, 291540, 311302, 331712

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OFFSET

1,1

COMMENTS

The identity (324*n-1)^2-(324*n^2-2*n)*(18)^2=1 can be written as A158306(n)^2-a(n)*(18)^2=1.

LINKS

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

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

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*(18^2*t-2)).

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

FORMULA

Contribution from Harvey P. Dale, Jul 14 2011: (Start)

G.f.: -2*x*(163*x+161)/(x-1)^3.

a(1)=322, a(2)=1292, a(3)=2910, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). (End)

MATHEMATICA

Table[324n^2-2n, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {322, 1292, 2910}, 40] (* Harvey P. Dale, Jul 14 2011 *)

PROG

(Magma) I:=[322, 1292, 2910]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];

(PARI) a(n) = 324*n^2 - 2*n.

CROSSREFS

Cf. A158306.