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A174443 Generating function x/(1+4*x-8*x^2). 2

%I

%S 0,1,-4,24,-128,704,-3840,20992,-114688,626688,-3424256,18710528,

%T -102236160,558628864,-3052404736,16678649856,-91133837312,

%U 497964548096,-2720928890880,14867431948288,-81237158920192,443888091267072,-2425449636429824,13252903275855872

%N Generating function x/(1+4*x-8*x^2).

%C Binet form: with a = 4/(1 + sqrt(3)); b = 4/(1 - sqrt(3)); we have a(n)=(a^n - b^n)/(a - b).

%C Alternative expressions for the roots are -2 +- 2*sqrt(3).

%C Limiting ratio a(n+1)/a(n) is:-5.464101615137755== -2-2*sqrt(3).

%H Nathaniel Johnston, <a href="/A174443/b174443.txt">Table of n, a(n) for n = 0..500</a>

%F a(0)=0, a(1)=1, a(n) = -4a(n-1) + 8a(n-2).

%F a(0)=0, a(n) = (-2)^(n-1)*A002605(n).

%t a = 4/(1 + Sqrt[3]); b = 4/(1 - Sqrt[3]);

%t f[n_] = (a^n - b^n)/(a - b);

%t Table[FullSimplify[f[n]], {n, 0, 30}]

%Y Cf. A180222 (unsigned version of this sequence).

%K sign,easy

%O 0,3

%A _Roger L. Bagula_, Nov 28 2010

%E Correction of the Mathematica code and better name by _Joerg Arndt_.

%E Formulae and edited by _Ralf Stephan_, Nov 27 2010

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Last modified June 6 17:28 EDT 2020. Contains 334830 sequences. (Running on oeis4.)