A157961 - OEIS

A157961

a(n) = 242*n - 1.

241, 483, 725, 967, 1209, 1451, 1693, 1935, 2177, 2419, 2661, 2903, 3145, 3387, 3629, 3871, 4113, 4355, 4597, 4839, 5081, 5323, 5565, 5807, 6049, 6291, 6533, 6775, 7017, 7259, 7501, 7743, 7985, 8227, 8469, 8711, 8953, 9195, 9437, 9679, 9921, 10163

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The identity (242*n - 1)^2 - (121*n^2 - n)*22^2 = 1 can be written as a(n)^2 - A157960(n)*22^2 = 1. - Vincenzo Librandi, Feb 10 2012

LINKS

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

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 14 in the first table at p. 85, case d(t) = t*(11^2*t-1)).

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

FORMULA

G.f.: x*(x+241)/(x-1)^2. - Vincenzo Librandi, Feb 10 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 10 2012

MATHEMATICA

LinearRecurrence[{2, -1}, {241, 483}, 50] (* Vincenzo Librandi, Feb 10 2012 *)

242*Range[50]-1 (* Harvey P. Dale, Aug 27 2020 *)

PROG

(Magma) I:=[241, 483]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 10 2012

(PARI) for(n=1, 50, print1(242*n - 1", ")); \\ Vincenzo Librandi, Feb 10 2012

CROSSREFS

Cf. A157960.