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A166917 a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 85, a(1) = 1364.

%I A166917 #14 Oct 03 2024 06:32:15
%S A166917 85,1364,21840,349504,5592320,89478144,1431654400,22906486784,
%T A166917 366503854080,5864061927424,93824991887360,1501199874392064,
%U A166917 24019198007050240,384307168179912704,6148914691147038720,98382635059426361344,1574122160955116748800,25185954575299047849984
%N A166917 a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 85, a(1) = 1364.
%C A166917 Related to Reverse and Add trajectory of 318 in base 4: A075153(6*n+5) = 240*a(n).
%H A166917 G. C. Greubel, <a href="/A166917/b166917.txt">Table of n, a(n) for n = 0..500</a>
%H A166917 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20, -64).
%F A166917 a(n) = (256*16^n - 4^n)/3.
%F A166917 G.f.: (85 - 336*x)/((1-4*x)*(1-16*x)).
%F A166917 Limit_{n -> infinity} a(n)/a(n-1) = 16.
%F A166917 E.g.f.: (1/3)*(256*exp(16*x) - exp(4*x)). - _G. C. Greubel_, May 28 2016
%t A166917 LinearRecurrence[{20,-64}, {85, 1364}, 50] (* _G. C. Greubel_, May 28 2016 *)
%o A166917 (PARI) {m=15; v=concat([85, 1364], vector(m-2)); for(n=3, m, v[n]=20*v[n-1]-64*v[n-2]); v}
%o A166917 (Magma)
%o A166917 [Binomial(4^(n+4), 2)/384: n in [0..30]]; // _G. C. Greubel_, Oct 02 2024
%o A166917 (SageMath)
%o A166917 A166917=BinaryRecurrenceSequence(20,-64,85,1364)
%o A166917 [A166917(n) for n in range(31)] # _G. C. Greubel_, Oct 02 2024
%Y A166917 Cf. A075153, A166912, A166913, A166914, A166915, A166916, A166927, A166965, A166984.
%K A166917 nonn,easy
%O A166917 0,1
%A A166917 _Klaus Brockhaus_, Oct 27 2009