%I #23 May 31 2020 12:40:31
%S 1,4,12,48,144,576,1728,6912,20736,82944,248832,995328,2985984,
%T 11943936,35831808,143327232,429981696,1719926784,5159780352,
%U 20639121408,61917364224,247669456896,743008370688,2972033482752,8916100448256,35664401793024,106993205379072,427972821516288
%N Start with 1; multiply alternately by 4 and 3.
%C Satisfies Benford's law.
%D Berger, Arno, and Theodore P. Hill. "Benford's law strikes back: no simple explanation in sight for mathematical gem." The Mathematical Intelligencer 33.1 (2011): 85-91.
%H Colin Barker, <a href="/A282023/b282023.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Be#Benford">Index entries for sequences related to Benford's law</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,12).
%F From _Ilya Gutkovskiy_, Feb 09 2017: (Start)
%F O.g.f.: (1 + 4*x)/(1 - 12*x^2).
%F E.g.f.: 2*sinh(2*sqrt(3)*x)/sqrt(3) + cosh(2*sqrt(3)*x).
%F (End)
%F From _Colin Barker_, Feb 09 2017: (Start)
%F a(n) = 2^n * 3^(n/2) for n even.
%F a(n) = 2^(n+1) * 3^((n-1)/2) for n odd.
%F a(n) = 12*a(n-2) for n>1.
%F (End)
%t CoefficientList[Series[(4 x + 1)/(-12 x^2 + 1), {x, 0, 27}], x] (* or *)
%t Range[0, 27]! CoefficientList[ Series[2 Sinh[2 Sqrt[3]*x]/Sqrt[3] + Cosh[2 Sqrt[3]*x], {x, 0, 27}], x] (* or *)
%t LinearRecurrence[{0, 12}, {1, 4}, 28] (* _Robert G. Wilson v_, Feb 09 2017 *)
%t nxt[{a_,b_}]:=If[b/a==3,{b,4b},{b,3b}]; NestList[nxt,{1,4},30][[All,1]] (* _Harvey P. Dale_, May 31 2020 *)
%o (PARI) Vec((1 + 4*x)/(1 - 12*x^2) + O(x^30)) \\ _Colin Barker_, Feb 09 2017
%o (PARI) a(n)=2^if(n%2,n+1,n)*3^(n\2) \\ _Charles R Greathouse IV_, Feb 09 2017
%Y Cf. A282022.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Feb 08 2017