A157738 18522n - 42.

18480, 37002, 55524, 74046, 92568, 111090, 129612, 148134, 166656, 185178, 203700, 222222, 240744, 259266, 277788, 296310, 314832, 333354, 351876, 370398, 388920, 407442, 425964, 444486, 463008, 481530, 500052, 518574, 537096, 555618

Offset

1,1

Comments

The identity (388962*n^2-1764*n+1)^2-(441*n^2-2*n)*(18522*n-42)^2=1 can be written as A157739(n)^2-A157737(n)*a(n)^2=1. - Vincenzo Librandi, Jan 25 2012

This is the case s=21 of the identity (2*s^4*n^2-4*s^2*n+1)^2-(s^2*n^2-2*n)*(2*s^3*n-2*s)^2=1. - Bruno Berselli, Feb 05 2011

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

G.f.: x*(18480+42*x)/(x-1)^2. - Vincenzo Librandi, Jan 25 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 25 2012

Maple

A157738:=n->18522*n - 42; seq(A157738(n), n=1..40); # Wesley Ivan Hurt, Feb 26 2014

Mathematica

LinearRecurrence[{2, -1}, {18480, 37002}, 40] (* Vincenzo Librandi, Jan 25 2012 *)

Prog

(Magma) I:=[18480, 37002]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]]; // Vincenzo Librandi, Jan 25 2012
(PARI) for(n=1, 22, print1(18522*n - 42", ")); \\ Vincenzo Librandi, Jan 25 2012

Crossrefs

Cf. A157737, A157739.

Sequence in context: A035924 A209895 A190110 * A247205 A173274 A237012

Adjacent sequences: A157735 A157736 A157737 * A157739 A157740 A157741

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 05 2009

Status

approved