OFFSET
0,1
COMMENTS
The identity (6561*n^2 - 3564*n + 485)^2 - (81*n^2 - 44*n + 6)*(729*n - 198)^2 = 1 can be written as A156774(n)^2 - a(n)*A156772(n)^2 = 1 for n > 0.
For n >= 1, the continued fraction expansion of sqrt(a(n)) is [9n-3; {1, 1, 3, 1, 9n-4, 1, 3, 1, 1, 18n-6}]. - Magus K. Chu, Sep 13 2022
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
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.: (6 + 25*x + 131*x^2)/(1-x)^3.
E.g.f.: (6 + 37*x + 81*x^2)*exp(x). - Elmo R. Oliveira, Oct 19 2024
MAPLE
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {6, 43, 242}, 40]
Table[81n^2-44n+6, {n, 0, 40}] (* Harvey P. Dale, Oct 29 2019 *)
PROG
(Magma) [81*n^2 - 44*n + 6: n in [0..40] ];
(PARI) a(n)=81*n^2-44*n+6 \\ Charles R Greathouse IV, Dec 23 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 15 2009
EXTENSIONS
Edited by Charles R Greathouse IV, Jul 25 2010
STATUS
approved