A158271 324n^2 + 2n.

326, 1300, 2922, 5192, 8110, 11676, 15890, 20752, 26262, 32420, 39226, 46680, 54782, 63532, 72930, 82976, 93670, 105012, 117002, 129640, 142926, 156860, 171442, 186672, 202550, 219076, 236250, 254072, 272542, 291660, 311426, 331840

Offset

1,1

Comments

The identity (324*n+1)^2-(324*n^2+2*n)*(18)^2=1 can be written as A158272(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

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

G.f.: x*(-322*x-326)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {326, 1300, 2922}, 50]

Prog

(Magma) I:=[326, 1300, 2922]; [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. A158272.

Sequence in context: A066128 A138816 A138817 * A203723 A097737 A236822

Adjacent sequences: A158268 A158269 A158270 * A158272 A158273 A158274

Keyword

nonn,easy,changed

Author

Vincenzo Librandi, Mar 15 2009

Status

approved