cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A299915 #27 Sep 08 2022 08:46:20
%S A299915 0,1,9,69,513,3789,27945,206037,1518993,11198493,82558521,608644773,
%T A299915 4487100705,33080169069,243876313161,1797924789621,13254807348657,
%U A299915 97718168662461,720405829778265,5311034444054853,39154440039154497,288657547023732237,2128064642743736169
%N A299915 a(n) = A299914(2n).
%D A299915 Murat Sahin and Elif Tan, Conditional (strong) divisibility sequences, Fib. Q., 56 (No. 1, 2018), 18-31.
%H A299915 Vincenzo Librandi, <a href="/A299915/b299915.txt">Table of n, a(n) for n = 0..200</a>
%H A299915 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-12)
%F A299915 G.f.: x/(12*x^2-9*x+1). - _Alois P. Heinz_, Mar 10 2018
%F A299915 From _Colin Barker_, Mar 12 2018: (Start)
%F A299915 a(n) = (-((9-sqrt(33))/2)^n + ((9+sqrt(33))/2)^n) / sqrt(33).
%F A299915 a(n) = 9*a(n-1) - 12*a(n-2) for n>1.
%F A299915 (End)
%F A299915 E.g.f.: 2*exp(9*x/2)*sinh(sqrt(33)*x/2)/sqrt(33). - _Stefano Spezia_, Dec 24 2021
%p A299915 a:= n-> (<<0|1>, <-12|9>>^n)[1, 2]:
%p A299915 seq(a(n), n=0..25);  # _Alois P. Heinz_, Mar 10 2018
%t A299915 CoefficientList[Series[x/(12 x^2 - 9 x + 1), {x, 0, 21}], x] (* _Michael De Vlieger_, Mar 10 2018 *)
%t A299915 LinearRecurrence[{9, -12}, {0, 1}, 30] (* _Vincenzo Librandi_, Mar 11 2018 *)
%o A299915 (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 A299915 (PARI) concat(0, Vec(x / (12*x^2-9*x+1) + O(x^30))) \\ _Colin Barker_, Mar 12 2018
%Y A299915 Cf. A299914.
%K A299915 nonn,easy
%O A299915 0,3
%A A299915 _N. J. A. Sloane_, Mar 10 2018
%E A299915 More terms from _Altug Alkan_, Mar 10 2018