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A114542
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Vector Matrix Markov that approximates the atomic fine structure constant.
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0
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0, 1, 1, 4691, 14080, 22014870, 110093079, 103403952290, 723144248019, 486101604111121, 4363129375507939, 2287092226229919002, 25031447861507056918, 10769715054951194077653, 138896030830402313512116
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| 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}}
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FORMULA
| M = {{0, 1, 0}, {0, 0, 1}, {9389, 4691, 0}} w[n]=M.w[n-1] a(n) = w[n][[1]]
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MATHEMATICA
| 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}]]
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CROSSREFS
| Sequence in context: A022244 A190131 A204073 * A114568 A107544 A092375
Adjacent sequences: A114539 A114540 A114541 * A114543 A114544 A114545
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Feb 15 2006
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