OFFSET
1,1
COMMENTS
The identity (5000*n^2 + 200*n + 1)^2 - (25*n^2 + n)*(1000*n + 20)^2 = 1 can be written as A157511(n)^2 - a(n)*A157510(n)^2 = 1. This is the case s=5 of the identity (8*n^2*s^4 + 8*n*s^2 + 1)^2 -(n^2*s^2 + n)*(8*n*s^3 + 4*s)^2 = 1. - Vincenzo Librandi, Feb 04 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*(-26 - 24*x)/(x-1)^3. - Vincenzo Librandi, Feb 04 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 04 2012
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {26, 102, 228}, 50] (* Vincenzo Librandi, Feb 04 2012 *)
Table[25n^2+n, {n, 50}] (* Harvey P. Dale, Sep 15 2024 *)
PROG
(Magma) [ 25*n^2+n: n in [1..50] ];
(PARI) for(n=1, 40, print1(25*n^2 + n", ")); \\ Vincenzo Librandi, Feb 04 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Nov 22 2010
STATUS
approved