OFFSET
1,1
COMMENTS
The identity (388962*n^2 - 347508*n + 77617)^2 - (441*n^2 - 394*n + 88)*(18522*n - 8274)^2 = 1 can be written as A157736(n)^2 - a(n)*A157735(n)^2 = 1.
441*a(n) + 1 is a square. - Bruno Berselli, Apr 23 2018
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: x*(135 + 659*x + 88*x^2)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
a(n) = (9*n - 4)*(49*n - 22). - Bruno Berselli, Apr 23 2018
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {135, 1064, 2875}, 40]
PROG
(Magma) I:=[135, 1064, 2875]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n) = 441*n^2 - 394*n + 88.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 05 2009
STATUS
approved