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a(n) = A299914(2n).
4

%I #27 Sep 08 2022 08:46:20

%S 0,1,9,69,513,3789,27945,206037,1518993,11198493,82558521,608644773,

%T 4487100705,33080169069,243876313161,1797924789621,13254807348657,

%U 97718168662461,720405829778265,5311034444054853,39154440039154497,288657547023732237,2128064642743736169

%N a(n) = A299914(2n).

%D Murat Sahin and Elif Tan, Conditional (strong) divisibility sequences, Fib. Q., 56 (No. 1, 2018), 18-31.

%H Vincenzo Librandi, <a href="/A299915/b299915.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-12)

%F G.f.: x/(12*x^2-9*x+1). - _Alois P. Heinz_, Mar 10 2018

%F From _Colin Barker_, Mar 12 2018: (Start)

%F a(n) = (-((9-sqrt(33))/2)^n + ((9+sqrt(33))/2)^n) / sqrt(33).

%F a(n) = 9*a(n-1) - 12*a(n-2) for n>1.

%F (End)

%F E.g.f.: 2*exp(9*x/2)*sinh(sqrt(33)*x/2)/sqrt(33). - _Stefano Spezia_, Dec 24 2021

%p a:= n-> (<<0|1>, <-12|9>>^n)[1, 2]:

%p seq(a(n), n=0..25); # _Alois P. Heinz_, Mar 10 2018

%t CoefficientList[Series[x/(12 x^2 - 9 x + 1), {x, 0, 21}], x] (* _Michael De Vlieger_, Mar 10 2018 *)

%t LinearRecurrence[{9, -12}, {0, 1}, 30] (* _Vincenzo Librandi_, Mar 11 2018 *)

%o (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

%o (PARI) concat(0, Vec(x / (12*x^2-9*x+1) + O(x^30))) \\ _Colin Barker_, Mar 12 2018

%Y Cf. A299914.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Mar 10 2018

%E More terms from _Altug Alkan_, Mar 10 2018