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A190970 a(n) = 5*a(n-1) - 9*a(n-2), with a(0)=0, a(1)=1.

%I A190970 #28 Dec 16 2023 20:24:08
%S A190970 0,1,5,16,35,31,-160,-1079,-3955,-10064,-14725,16951,217280,933841,
%T A190970 2713685,5163856,1396115,-39494129,-210035680,-694731239,-1583335075,
%U A190970 -1664094224,5929544555,44624570791,169756952960,447163627681,708005561765,-484444840304
%N A190970 a(n) = 5*a(n-1) - 9*a(n-2), with a(0)=0, a(1)=1.
%H A190970 G. C. Greubel, <a href="/A190970/b190970.txt">Table of n, a(n) for n = 0..1000</a>
%H A190970 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9).
%F A190970 G.f.: x/(1 - 5*x + 9*x^2). - _Philippe Deléham_, Oct 12 2011
%F A190970 a(n) = 3^(n-1) * ChebyshevU(n-1, 5/6). - _G. C. Greubel_, Jun 09 2022
%p A190970 A190970 := proc(n)
%p A190970     option remember ;
%p A190970     if n <= 1 then
%p A190970         n;
%p A190970     else
%p A190970         5*procname(n-1)-9*procname(n-2) ;
%p A190970     end if;
%p A190970 end proc: # _R. J. Mathar_, Mar 23 2023
%t A190970 LinearRecurrence[{5,-9}, {0,1}, 50]
%o A190970 (Magma) [n le 2 select n-1 else 5*Self(n-1) - 9*Self(n-2): n in [1..51]]; // _G. C. Greubel_, Jun 09 2022
%o A190970 (Sage) [3^(n-1)*chebyshev_U(n-1, 5/6) for n in (0..50)] # _G. C. Greubel_, Jun 09 2022
%Y A190970 Cf. A190958 (index to generalized Fibonacci sequences).
%K A190970 sign,easy
%O A190970 0,3
%A A190970 _Vladimir Joseph Stephan Orlovsky_, May 24 2011