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A190979 a(n) = 9*a(n-1) - 2*a(n-2), with a(0)=0, a(1)=1.

%I A190979 #49 Aug 26 2022 10:26:55
%S A190979 0,1,9,79,693,6079,53325,467767,4103253,35993743,315737181,2769647143,
%T A190979 24295349925,213118855039,1869478995501,16399073249431,
%U A190979 143852701253877,1261876164786031,11069180080566525,97098868395526663,851751455398606917,7471565361796408927
%N A190979 a(n) = 9*a(n-1) - 2*a(n-2), with a(0)=0, a(1)=1.
%C A190979 a(n+1) equals the number of words of length n over {0,1,2,3,4,5,6,7,8} avoiding 01 and 02. - _Milan Janjic_, Dec 17 2015
%H A190979 Colin Barker, <a href="/A190979/b190979.txt">Table of n, a(n) for n = 0..1000</a>
%H A190979 Tomislav Doslic, <a href="http://dx.doi.org/10.1007/s10910-013-0167-2">Planar polycyclic graphs and their Tutte polynomials</a>, Journal of Mathematical Chemistry, Volume 51, Issue 6, 2013, pp. 1599-1607. See Cor. 3.7(e).
%H A190979 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-2).
%F A190979 a(n) = ((9/2 + 1/2*sqrt(73))^n - (9/2 - 1/2*sqrt(73))^n)/sqrt(79). - _Giorgio Balzarotti_, May 27 2011
%F A190979 G.f.: x / (1-9*x+2*x^2). - _Colin Barker_, Feb 26 2016
%F A190979 From _G. C. Greubel_, Jun 17 2022: (Start)
%F A190979 a(n) = 2^((n-1)/2)*ChebyshevU(n-1, 9*x/(2*sqrt(2))).
%F A190979 E.g.f.: (2/sqrt(73))*exp(9*x/2)*sinh(sqrt(73)*x/2). (End)
%t A190979 LinearRecurrence[{9,-2}, {0,1}, 50]
%o A190979 (Magma) I:=[0,1]; [n le 2 select I[n] else 10*Self(n-1)-2*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Dec 17 2015
%o A190979 (PARI) concat(0, Vec(x/(1-9*x+2*x^2) + O(x^30))) \\ _Colin Barker_, Feb 26 2016
%o A190979 (SageMath)
%o A190979 A190979 = BinaryRecurrenceSequence(9,-2,0,1)
%o A190979 [A190979(n) for n in (0..30)] # _G. C. Greubel_, Jun 17 2022
%Y A190979 Cf. A190958 (index to generalized Fibonacci sequences).
%K A190979 nonn,easy
%O A190979 0,3
%A A190979 _Vladimir Joseph Stephan Orlovsky_, May 24 2011