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A166965 a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 1, a(1) = 19.

%I A166965 #12 Sep 08 2022 08:45:48
%S A166965 1,19,316,5104,81856,1310464,20970496,335540224,5368692736,
%T A166965 85899280384,1374389272576,21990231506944,351843716694016,
%U A166965 5629499517435904,90071992480301056,1441151880490123264,23058430091063197696
%N A166965 a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 1, a(1) = 19.
%C A166965 lim_{n -> infinity} a(n)/a(n-1) = 16.
%H A166965 Vincenzo Librandi, <a href="/A166965/b166965.txt">Table of n, a(n) for n = 0..200</a>
%H A166965 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20, -64).
%F A166965 a(n) = (5*16^n - 4^n)/4.
%F A166965 G.f.: (1-x)/((1-4*x)*(1-16*x)).
%F A166965 E.g.f.: (1/4)*(5*exp(16*x) - exp(4*x)). - _G. C. Greubel_, May 29 2016
%t A166965 LinearRecurrence[{20,-64},{1,19},20] (* _Harvey P. Dale_, Aug 24 2014 *)
%o A166965 (Magma) [ n le 2 select 18*n-17 else 20*Self(n-1)-64*Self(n-2): n in [1..17] ];
%Y A166965 Cf. A166927, A006105 (Gaussian binomial coefficient [ n, 2 ] for q=4).
%K A166965 nonn
%O A166965 0,2
%A A166965 _Klaus Brockhaus_, Oct 25 2009