OFFSET
1,1
COMMENTS
The identity (10368*n^2 + 288*n + 1)^2 - (36*n^2 + n)*(1728*n + 24)^2 = 1 can be written as A157326(n)^2 - a(n)*A157325(n)^2 = 1.
This is the case s=6 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, Jan 26 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
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 26 2012
G.f.: x*(-37 - 35*x)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {37, 146, 327}, 50] (* Vincenzo Librandi, Jan 26 2012 *)
Table[36n^2+n, {n, 50}] (* Harvey P. Dale, Mar 09 2019 *)
PROG
(Magma) I:=[37, 146, 327]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 26 2012
(PARI) for(n=1, 40, print1(36*n^2 + n", ")); \\ Vincenzo Librandi, Jan 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 27 2009
STATUS
approved