%I A114542
%S A114542 0,1,1,4691,14080,22014870,110093079,103403952290,723144248019,
%T A114542 486101604111121,4363129375507939,2287092226229919002,
%U A114542 25031447861507056918,10769715054951194077653,138896030830402313512116
%N A114542 Vector Matrix Markov that approximates the atomic fine structure constant.
%C A114542 The twice the ratio approaches 1/alpha: b = Table[2*N[a[[n + 1]]/a[[n]]], 
               {n, 2, 200}] The characteristic polynomial is a Pisot : 9389 + 4691* 
               x - x^3 NSolve[Det[M - IdentityMatrix[3]*x] == 0, x] {{x -> -67.4673}, 
               {x -> -2.00321}, {x -> 69.4705}}
%F A114542 M = {{0, 1, 0}, {0, 0, 1}, {9389, 4691, 0}} w[n]=M.w[n-1] a(n) = w[n][[1]]
%t A114542 M = {{0, 1, 0}, {0, 0, 1}, {9389, 4691, 0}} w[0] = {0, 1, 1} w[n_] := 
               w[n] = M.w[n - 1] a = Flatten[Table[w[n][[1]], {n, 0, 25}]]
%Y A114542 Sequence in context: A062626 A066731 A022244 this_sequence A114568 A107544 
               A092375
%Y A114542 Adjacent sequences: A114539 A114540 A114541 this_sequence A114543 A114544 
               A114545
%K A114542 nonn,uned
%O A114542 0,4
%A A114542 Roger Bagula (rlbagulatftn(AT)yahoo.com), Feb 15 2006