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%I #14 Jun 13 2015 00:53:37
%S 1,2,8,12,60,84,444,612,3276,4500,24156,33156,178092,244404,1312956,
%T 1801764,9679500,13283028,71360028,97926084,526086252,721938420,
%U 3878455932,5322332772,28593068364,39237733908,210796144092
%N Expansion of x*( 1+2*x-x^2-6*x^3 ) / ( 1-9*x^2+12*x^4 ).
%C The ratio a(n+1)/a(n) alternates between 5.3722813232690143299 and 1.3722813232690143299.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,9,0,-12).
%F Given the auxiliary b(0)=b(1)=1 and b(n) = b(n-1)/2 + b(n-2) *sqrt(5-(-1)^n*4) /2, a(n) =2^(n-1)*b(n).
%F a(n) = a(n-1)+6*a(n-2) if n is odd. a(n) = a(n-1)+2*a(n-2) if n is even. - _R. J. Mathar_, Jun 18 2014
%t a[1] := 1;a[2]=1;
%t a[n_] := a[n] = a[n - 1]/2 +a[n - 2]*Sqrt[(5 + 4*(-1)^(n - 1))]//2:
%t Table[2^(n - 1)*a[n], {n, 1, 30}]
%K nonn,easy
%O 1,2
%A _Roger L. Bagula_, Apr 29 2010
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