cp's OEIS Frontend

A166914 a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 21, a(1) = 340.

%I A166914 #21 Oct 03 2024 06:17:16
%S A166914 21,340,5456,87360,1398016,22369280,357912576,5726617600,91625947136,
%T A166914 1466015416320,23456247709696,375299967549440,6004799497568256,
%U A166914 96076792028200960,1537228672719650816,24595658764588154880
%N A166914 a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 21, a(1) = 340.
%C A166914 Related to Reverse and Add trajectory of 318 in base 4: A075153(6*n+2) = 240*a(n).
%H A166914 G. C. Greubel, <a href="/A166914/b166914.txt">Table of n, a(n) for n = 0..500</a>
%H A166914 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-64).
%F A166914 a(n) = (64*16^n - 4^n)/3.
%F A166914 G.f.: (21 - 80*x)/((1-4*x)*(1-16*x)).
%F A166914 Limit_{n -> infinity} a(n)/a(n-1) = 16.
%F A166914 From _G. C. Greubel_, May 28 2016: (Start)
%F A166914 a(n) = 20*a(n-1) - 64*a(n-2).
%F A166914 E.g.f.: (1/3)*(-exp(4*x) + 64*exp(16*x)). (End)
%t A166914 CoefficientList[Series[(21-80x)/((1-4x)(1-16x)),{x,0,20}],x]  (* or *) LinearRecurrence[{20,-64},{21,340},20] (* _Harvey P. Dale_, Feb 23 2011 & Mar 30 2012 *)
%o A166914 (PARI) {m=15; v=concat([21, 340], vector(m-2)); for(n=3, m, v[n]=20*v[n-1]-64*v[n-2]); v}
%o A166914 (Magma)
%o A166914 [Binomial(4^(n+3), 2)/96: n in [0..30]]; // _G. C. Greubel_, Oct 02 2024
%o A166914 (SageMath)
%o A166914 A166914=BinaryRecurrenceSequence(20,-64,21,340)
%o A166914 [A166914(n) for n in range(31)] # _G. C. Greubel_, Oct 02 2024
%Y A166914 Cf. A075153, A166912, A166913, A166915, A166916, A166917, A166927, A166965, A166984.
%K A166914 nonn
%O A166914 0,1
%A A166914 _Klaus Brockhaus_, Oct 27 2009