OFFSET
1,1
COMMENTS
The identity (625*n+1)^2-(625*n^2+2*n)*(25)^2=1 can be written as a(n)^2-A158382(n)*(25)^2=1.
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*(25^2*t+2)).
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
G.f.: x*(626-x)/(1-x)^2.
a(n) = 2*a(n-1)-a(n-2).
MATHEMATICA
LinearRecurrence[{2, -1}, {626, 1251}, 50]
625*Range[40]+1 (* Harvey P. Dale, Mar 14 2018 *)
PROG
I:=[626, 1251]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 625*n + 1.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 17 2009
STATUS
approved