A157508 a(n) = 1458*n - 18.

1440, 2898, 4356, 5814, 7272, 8730, 10188, 11646, 13104, 14562, 16020, 17478, 18936, 20394, 21852, 23310, 24768, 26226, 27684, 29142, 30600, 32058, 33516, 34974, 36432, 37890, 39348, 40806, 42264, 43722, 45180, 46638, 48096, 49554

Offset

1,1

Comments

The identity (13122*n^2 - 324*n + 1)^2 - (81*n^2 - 2*n)*(1458*n - 18)^2 = 1 can be written as A157509(n)^2 - A157507(n)*a(n)^2 = 1 (see also second comment at A157509). - Vincenzo Librandi, Jan 26 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 (2,-1).

Formula

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 26 2012

G.f.: 18*(82*x-1)/(x-1)^2. - Vincenzo Librandi, Jan 26 2012 [corrected by Georg Fischer, May 11 2019]

Mathematica

LinearRecurrence[{2, -1}, {1440, 2898}, 40] (* Vincenzo Librandi, Jan 26 2012 *)

Prog

(Magma) I:=[1440, 2898]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 26 2012
(PARI) for(n=1, 35, print1(1458*n - 18", ")); \\ Vincenzo Librandi, Jan 26 2012

Crossrefs

Cf. A157507, A157509.

Sequence in context: A252186 A179691 A078095 * A061221 A238041 A187291

Adjacent sequences: A157505 A157506 A157507 * A157509 A157510 A157511

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 02 2009

Status

approved