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A166912 a(n) = 20*a(n-1) - 64*a(n-2) - 225 for n > 2; a(0) = 106, a(1) = 8075, a(2) = 114235.

%I A166912 #18 Oct 21 2022 22:10:03
%S A166912 106,8075,114235,1767675,28042235,447713275,7159562235,114537594875,
%T A166912 1832539914235,29320392212475,469125289738235,7506000693166075,
%U A166912 120095995320074235,1921535862038855675,30744573540292362235
%N A166912 a(n) = 20*a(n-1) - 64*a(n-2) - 225 for n > 2; a(0) = 106, a(1) = 8075, a(2) = 114235.
%C A166912 Related to Reverse and Add trajectory of 318 in base 4: A075153(6*n) = 3*a(n).
%C A166912 lim_{n -> infinity} a(n)/a(n-1) = 16.
%H A166912 G. C. Greubel, <a href="/A166912/b166912.txt">Table of n, a(n) for n = 0..500</a>
%H A166912 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21, -84, 64).
%F A166912 a(n) = (1280*16^n + 940*4^n - 15)/3 for n > 0.
%F A166912 G.f.: (106 + 5849*x - 46436*x^2 + 40256*x^3)/((1-x)*(1-4*x)*(1-16*x)).
%F A166912 From _G. C. Greubel_, May 28 2016: (Start)
%F A166912 a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3).
%F A166912 E.g.f.: (1/3)*(-15*exp(x) + 940*exp(4*x) + 1280*exp(16*x)) - 629. (End)
%t A166912 Join[{106},LinearRecurrence[{21,-84,64},{8075,114235,1767675},20]] (* _Harvey P. Dale_, Jun 07 2012 *)
%o A166912 (PARI) m=15; v=concat([106, 8075, 114235], vector(m-3)); for(n=4, m, v[n]=20*v[n-1]-64*v[n-2]-225); v
%Y A166912 Cf. A075153, A166913, A166914, A166915, A166916, A166917, A167120, A167121, A167122.
%K A166912 nonn,easy
%O A166912 0,1
%A A166912 _Klaus Brockhaus_, Oct 27 2009