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Search: id:A120464
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| A120464 |
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Sequence produced by 3 X 3 Markov chain based on Murskii's Cayley table for a three element groupoid: M = {{1,1,1},{1,1,1},{1,1,1}}+{{0,0,0},{0,0,1},{0,2,2}} = {{1, 1, 1}, {1, 1, 2}, {1, 3, 3}}. |
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+0
1
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| 0, 2, 11, 57, 292, 1495, 7653, 39176, 200543, 1026585, 5255116, 26901079, 137707341, 704927552, 3608542943, 18472227585, 94559825764, 484054270519, 2477886723189, 12684368234936, 64931619356831, 332386691572713
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Characteristic polynomial x^3-5*x^2+2. Roots: {-0.6874, 0.568373, 5.11903}. Ratio: 5.11903}
Lyndon (1951) earlier had proved every two-element algebra has a finitely based system of identities. However Murskii (1965) found this classic 3-element example (which is inherently not finitely based).
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LINKS
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Author?, Title?
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FORMULA
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Let M = {{1, 1, 1}, {1, 1, 2}, {1, 3, 3}}; v[1] = {0, 1, 1}; v[n] = M.v[n - 1]; then a(n) = v[n][[1]]
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MATHEMATICA
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M = {{1, 1, 1}, {1, 1, 2}, {1, 3, 3}} v[1] = {0, 1, 1} v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}] Det[M - x*IdentityMatrix[3]] Factor[%] aaa = Table[x /. NSolve[Det[M - x*IdentityMatrix[3]] == 0, x][[n]], {n, 1, 3}] Abs[aaa] a1 = Table[N[a[[n]]/a[[n - 1]]], {n, 7, 50}]
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CROSSREFS
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Sequence in context: A041129 A037490 A037570 this_sequence A054130 A037738 A037633
Adjacent sequences: A120461 A120462 A120463 this_sequence A120465 A120466 A120467
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Jul 01 2006
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EXTENSIONS
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Edited by njas, Jul 13 2007
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