A158272 324n + 1.

325, 649, 973, 1297, 1621, 1945, 2269, 2593, 2917, 3241, 3565, 3889, 4213, 4537, 4861, 5185, 5509, 5833, 6157, 6481, 6805, 7129, 7453, 7777, 8101, 8425, 8749, 9073, 9397, 9721, 10045, 10369, 10693, 11017, 11341, 11665, 11989, 12313, 12637, 12961

Offset

1,1

Comments

The identity (324*n+1)^2-(324*n^2+2*n)*(18)^2=1 can be written as a(n)^2-A158271(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 (2,-1).

Formula

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

G.f.: x*(325-x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {325, 649}, 50]

Prog

(Magma) I:=[325, 649]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 324*n + 1.

Crossrefs

Cf. A158271.

Sequence in context: A025304 A351801 A160580 * A183645 A299708 A031714

Adjacent sequences: A158269 A158270 A158271 * A158273 A158274 A158275

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 15 2009

Status

approved