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A167031 a(n) = 20*a(n-1) - 64*a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 20.

%I A167031 #9 Sep 08 2022 08:45:48
%S A167031 1,20,337,5461,87653,1403557,22461349,359399333,5750460325,
%T A167031 92007649189,1472123522981,23553980911525,376863712759717,
%U A167031 6029819476856741,96477111920512933,1543633791891427237,24698140674915717029
%N A167031 a(n) = 20*a(n-1) - 64*a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 20.
%C A167031 lim_{n -> infinity} a(n)/a(n-1) = 16.
%H A167031 Vincenzo Librandi, <a href="/A167031/b167031.txt">Table of n, a(n) for n = 0..200</a>
%H A167031 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-84,64).
%F A167031 a(n) = (241*16^n - 65*4^n + 4)/180.
%F A167031 G.f.: (1-x+x^2)/((1-x)*(1-4*x)*(1-16*x)).
%F A167031 From _G. C. Greubel_, May 30 2016: (Start)
%F A167031 a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-2).
%F A167031 E.g.f.: (1/180)*(241*exp(16*x) - 65*exp(4*x) + 4*exp(x)). (End)
%t A167031 LinearRecurrence[{21, -84, 64}, {1, 20, 337}, 50] (* _G. C. Greubel_, May 30 2016 *)
%o A167031 (Magma) [ n le 2 select 19*n-18 else 20*Self(n-1)-64*Self(n-2)+1: n in [1..17] ];
%Y A167031 Cf. A166915, A166916, A006105, A167032, A167033.
%K A167031 nonn
%O A167031 0,2
%A A167031 _Klaus Brockhaus_, Oct 27 2009