A157505 a(n) = 1458*n + 18.

1476, 2934, 4392, 5850, 7308, 8766, 10224, 11682, 13140, 14598, 16056, 17514, 18972, 20430, 21888, 23346, 24804, 26262, 27720, 29178, 30636, 32094, 33552, 35010, 36468, 37926, 39384, 40842, 42300, 43758, 45216, 46674, 48132, 49590

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 A157506(n)^2 - A177099(n)*a(n)^2 = 1 (see Bruno Berselli's comment at A177099). - Vincenzo Librandi, Feb 04 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

G.f.: x*(1476 - 18*x)/(1-x)^2. - Vincenzo Librandi, Feb 04 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 04 2012

Mathematica

LinearRecurrence[{2, -1}, {1476, 2934}, 50] (* Vincenzo Librandi, Feb 04 2012 *)
1458*Range[40]+18 (* Harvey P. Dale, Aug 17 2016 *)

Prog

(Magma) I:=[1476, 2934]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 04 2012
(PARI) for(n=1, 40, print1(1458n + 18", ")); \\ Vincenzo Librandi, Feb 04 2012

Crossrefs

Cf. A157506, A177099.

Sequence in context: A237144 A187310 A167575 * A290723 A187531 A251218

Adjacent sequences: A157502 A157503 A157504 * A157506 A157507 A157508

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 02 2009

Status

approved