OFFSET
1,1
COMMENTS
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).
G.f.: x*(7263026 + 63884459*x + 14945957*x^2)/(1-x)^3.
E.g.f.: (6561*x*(6561*x - 1171) + 14945957)*exp(x) - 14945957. - G. C. Greubel, Feb 04 2018
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {7263026, 85673537, 250177490}, 40]
Table[43046721*n^2 - 50729652*n + 14945957, {n, 1, 30}] (* G. C. Greubel, Feb 04 2018 *)
PROG
(Magma) I:=[7263026, 85673537, 250177490]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..30]];
(PARI) a(n) = 43046721*n^2 - 50729652*n + 14945957.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 28 2009, Mar 08 2009
STATUS
approved