OFFSET
0,3
REFERENCES
Murat Sahin and Elif Tan, Conditional (strong) divisibility sequences, Fib. Q., 56 (No. 1, 2018), 18-31.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (9,-12)
FORMULA
G.f.: x/(12*x^2-9*x+1). - Alois P. Heinz, Mar 10 2018
From Colin Barker, Mar 12 2018: (Start)
a(n) = (-((9-sqrt(33))/2)^n + ((9+sqrt(33))/2)^n) / sqrt(33).
a(n) = 9*a(n-1) - 12*a(n-2) for n>1.
(End)
E.g.f.: 2*exp(9*x/2)*sinh(sqrt(33)*x/2)/sqrt(33). - Stefano Spezia, Dec 24 2021
MAPLE
a:= n-> (<<0|1>, <-12|9>>^n)[1, 2]:
seq(a(n), n=0..25); # Alois P. Heinz, Mar 10 2018
MATHEMATICA
CoefficientList[Series[x/(12 x^2 - 9 x + 1), {x, 0, 21}], x] (* Michael De Vlieger, Mar 10 2018 *)
LinearRecurrence[{9, -12}, {0, 1}, 30] (* Vincenzo Librandi, Mar 11 2018 *)
PROG
(Magma) I:=[0, 1]; [n le 2 select I[n] else 9*Self(n-1)-12*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Mar 11 2018
(PARI) concat(0, Vec(x / (12*x^2-9*x+1) + O(x^30))) \\ Colin Barker, Mar 12 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 10 2018
EXTENSIONS
More terms from Altug Alkan, Mar 10 2018
STATUS
approved