A157441 a(n) = 1331*n - 1122.

209, 1540, 2871, 4202, 5533, 6864, 8195, 9526, 10857, 12188, 13519, 14850, 16181, 17512, 18843, 20174, 21505, 22836, 24167, 25498, 26829, 28160, 29491, 30822, 32153, 33484, 34815, 36146, 37477, 38808, 40139, 41470, 42801, 44132, 45463

Offset: 1

Author

Vincenzo Librandi, Mar 01 2009

Keywords

• nonn
• easy

Comments

The identity (14641*n^2 - 24684*n + 10405)^2 - (121*n^2 - 204*n + 86)*(1331*n - 1122)^2 = 1 can be written as A157442(n)^2 - A157440(n)*a(n)^2 = 1. - Vincenzo Librandi, Jan 29 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).

Crossrefs

Cf. A157440, A157442.

Programs

Magma

I:=[209, 1540]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 29 2012

Mathematica

LinearRecurrence[{2,-1},{209,1540},50] (* Vincenzo Librandi, Jan 29 2012 *)

PARI

for(n=1, 40, print1(1331*n - 1122", ")); \\ Vincenzo Librandi, Jan 29 2012

Formula

G.f.: x*(209 + 1122*x)/(x-1)^2. - Vincenzo Librandi, Jan 29 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 29 2012