OFFSET
1,1
COMMENTS
The identity (961*n-1)^2-(961*n^2-2*n)*(31)^2 = 1 can be written as A158412(n)^2-a(n)*(31)^2 = 1.
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 15 in the first table at p. 85, case d(t) = t*(31^2*t-2)).
Vincenzo Librandi, X^2-AY^2=1
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*(-959-963*x)/(x-1)^3.
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {959, 3840, 8643}, 50]
Table[961n^2-2n, {n, 40}] (* Harvey P. Dale, Aug 29 2022 *)
PROG
(Magma) I:=[959, 3840, 8643]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 961*n^2 - 2*n;
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 18 2009
STATUS
approved