A157954 - OEIS

A157954

162n - 1.

161, 323, 485, 647, 809, 971, 1133, 1295, 1457, 1619, 1781, 1943, 2105, 2267, 2429, 2591, 2753, 2915, 3077, 3239, 3401, 3563, 3725, 3887, 4049, 4211, 4373, 4535, 4697, 4859, 5021, 5183, 5345, 5507, 5669, 5831, 5993, 6155, 6317, 6479, 6641, 6803, 6965

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OFFSET

1,1

COMMENTS

The identity (162*n-1)^2-(81*n^2-n)*(18)^2=1 can be written as a(n)^2-A157953(n)*(16)^2=1. - Vincenzo Librandi, Jan 29 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*(9^2*t-1)).

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 29 2012

G.f.: x*(161+x)/(1-x)^2. - Vincenzo Librandi, Jan 29 2012

MAPLE

A157954:=n->162*n - 1; seq(A157954(n), n=1..50); # Wesley Ivan Hurt, Mar 06 2014

MATHEMATICA

LinearRecurrence[{2, -1}, {161, 323}, 50] (* Vincenzo Librandi, Jan 29 2012 *)

PROG

(Magma) I:=[161, 323]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 29 2012

(PARI) for(n=1, 40, print1(162*n - 1", ")); \\ Vincenzo Librandi, Jan 29 2012