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A167120 a(n) = 20*a(n-1) - 64*a(n-2) + 1 for n > 2; a(0) = 1, a(1) = 22, a(2) = 376.

%I A167120 #13 Aug 04 2025 12:22:38
%S A167120 1,22,376,6113,98197,1572709,25169573,402738085,6443909029,
%T A167120 103102943141,1649648684965,26394385338277,422310190927781,
%U A167120 6756963156905893,108111410918739877,1729782576332820389,27676521227857055653
%N A167120 a(n) = 20*a(n-1) - 64*a(n-2) + 1 for n > 2; a(0) = 1, a(1) = 22, a(2) = 376.
%C A167120 Lim_{n -> infinity} a(n)/a(n-1) = 16.
%H A167120 Vincenzo Librandi, <a href="/A167120/b167120.txt">Table of n, a(n) for n = 0..200</a>
%H A167120 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-84,64).
%F A167120 a(n) = (4321*16^n - 1460*4^n + 64)/2880, for n > 0.
%F A167120 G.f.: (1 + x - 2*x^2 + x^3)/((1-x)*(1-4*x)*(1-16*x)).
%F A167120 E.g.f.: (1/2880)*(-45 + 64*exp(x) - 1460*exp(4*x) + 4321*exp(16*x)). - _G. C. Greubel_, Jun 04 2016
%F A167120 a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3). - _Wesley Ivan Hurt_, Aug 04 2025
%t A167120 CoefficientList[Series[(1 + x - 2*x^2 + x^3)/((1 - x)*(1 - 4*x)*(1 - 16*x)), {x, 0, 10}], x] (* _G. C. Greubel_, Jun 04 2016 *)
%t A167120 LinearRecurrence[{21,-84,64},{1,22,376,6113},20] (* _Harvey P. Dale_, Jul 13 2018 *)
%o A167120 (Magma) [ n le 2 select 21*n-20 else n eq 3 select 376 else 20*Self(n-1)-64*Self(n-2)+1: n in [1..17] ];
%Y A167120 Cf. A166912, A166913, A167121, A167122.
%K A167120 nonn
%O A167120 0,2
%A A167120 _Klaus Brockhaus_, Oct 27 2009