OFFSET
1,1
COMMENTS
The identity (121*n + 1)^2 - (121*n^2 + 2*n)*11^2 = 1 can be written as A158131(n)^2 - a(n)*11^2 = 1 (see Barbeau's paper in link).
Also, the identity (29282*n^2 + 484*n + 1)^2 - (121*n^2 + 2*n)*(2662*n + 22)^2 = 1 can be written as A157614(n)^2 - a(n)*A157613(n)^2 = 1. - Vincenzo Librandi, Feb 21 2012
This last formula is the case s=11 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 21 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2-AY^2=1
E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(11^2*t+2)).
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(-119*x - 123)/(x-1)^3.
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {123, 488, 1095}, 50]
PROG
(Magma) [ n*(121*n+2): n in [1..40] ];
(PARI) a(n) = n*(121*n+2)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Nov 18 2010, Nov 19 2010
STATUS
approved