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*(48842 + 755975*x + 258065*x^2)/(1-x)^3.
E.g.f.: (258065 - 209223*x + 531441*x^2)*exp(x) - 258065. - G. C. Greubel, Nov 17 2018
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {48842, 902501, 2819042}, 40]
PROG
(Magma) I:=[48842, 902501, 2819042]; [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) = 531441*n^2 - 740664*n + 258065.
(Sage) [531441*n^2 - 740664*n + 258065 for n in (1..40)] # G. C. Greubel, Nov 17 2018
(GAP) List([1..40], n -> 531441*n^2 - 740664*n + 258065); # G. C. Greubel, Nov 17 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 04 2009
STATUS
approved