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A167033 a(n) = 20*a(n-1) - 64*a(n-2) + 3 for n > 1; a(0) = 1, a(1) = 22.

%I A167033 #10 Sep 08 2022 08:45:48
%S A167033 1,22,379,6175,99247,1589743,25443055,407117551,6513995503,
%T A167033 104224386799,1667592023791,26681479720687,426903704891119,
%U A167033 6830459395698415,109287350800936687,1748597614694035183,27977561842620755695
%N A167033 a(n) = 20*a(n-1) - 64*a(n-2) + 3 for n > 1; a(0) = 1, a(1) = 22.
%C A167033 lim_{n -> infinity} a(n)/a(n-1) = 16.
%H A167033 Vincenzo Librandi, <a href="/A167033/b167033.txt">Table of n, a(n) for n = 0..200</a>
%H A167033 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-84,64).
%F A167033 a(n) = (91*16^n - 35*4^n + 4)/60.
%F A167033 G.f.: (1+x+x^2)/((1-x)*(1-4*x)*(1-16*x)).
%F A167033 From _G. C. Greubel_, May 30 2016: (Start)
%F A167033 a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3).
%F A167033 E.g.f.: (1/60)*(91*exp(16*x) - 35*exp(4*x) + 4*exp(x)). (End)
%t A167033 LinearRecurrence[{21, -84, 64}, {1, 22, 379}, 50] (* _G. C. Greubel_, May 30 2016 *)
%o A167033 (Magma) [ n le 2 select 21*n-20 else 20*Self(n-1)-64*Self(n-2)+3: n in [1..17] ];
%Y A167033 Cf. A166915, A166916, A006105, A167031, A167032.
%K A167033 nonn
%O A167033 0,2
%A A167033 _Klaus Brockhaus_, Oct 27 2009