OFFSET
1,1
COMMENTS
The identity (484*n-1)^2-(484*n^2-2*n)*(22)^2=1 can be written as A158330(n)^2-a(n)*(22)^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*(22^2*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*(-482-486*x)/(x-1)^3.
E.g.f.: 2*exp(x)*x*(241 + 242*x). - Stefano Spezia, Aug 31 2024
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {482, 1932, 4350}, 50]
PROG
(Magma) I:=[482, 1932, 4350]; [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) = 484*n^2 - 2*n
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 16 2009
STATUS
approved