A157267 - OEIS

A157267

a(n) = 10368*n^2 - 4896*n + 577.

6049, 32257, 79201, 146881, 235297, 344449, 474337, 624961, 796321, 988417, 1201249, 1434817, 1689121, 1964161, 2259937, 2576449, 2913697, 3271681, 3650401, 4049857, 4470049, 4910977, 5372641, 5855041, 6358177, 6882049

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OFFSET

1,1

COMMENTS

The identity (10368*n^2 - 4896*n + 577)^2 - (36*n^2 - 17*n + 2)*(1728*n - 408)^2 = 1 can be written as a(n)^2 - A157265(n)*A157266(n)^2 = 1. - Vincenzo Librandi, Jan 27 2012

This is the case s=4n-1 of the identity (2*r^2 - 1)^2 - ((r^2 - 1)/144)*(24r)^2 = 1, where r = 18*s + 9*i^(s*(s+1)) - (-1)^s - 9 and i=sqrt(-1). - Bruno Berselli, 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 (3,-3,1).

FORMULA

G.f.: x*(-6049 - 14110*x - 577*x^2)/(x-1)^3. - Vincenzo Librandi, Jan 27 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 27 2012

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {6049, 32257, 79201}, 40] (* Vincenzo Librandi, Jan 27 2012 *)

PROG

(Magma) I:=[6049, 32257, 79201]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 27 2012

(PARI) for(n=1, 40, print1(10368*n^2 - 4896*n + 577", ")); \\ Vincenzo Librandi, Jan 27 2012