A299915 a(n) = A299914(2n).

0, 1, 9, 69, 513, 3789, 27945, 206037, 1518993, 11198493, 82558521, 608644773, 4487100705, 33080169069, 243876313161, 1797924789621, 13254807348657, 97718168662461, 720405829778265, 5311034444054853, 39154440039154497, 288657547023732237, 2128064642743736169

Offset: 0

Author

N. J. A. Sloane, Mar 10 2018

Keywords

• nonn
• easy

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)

Crossrefs

Cf. A299914.

Programs

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

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 *)

PARI

concat(0, Vec(x / (12*x^2-9*x+1) + O(x^30))) \\ Colin Barker, Mar 12 2018

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

Extensions

More terms from Altug Alkan, Mar 10 2018