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 A120464 a(n) = 5*a(n-1)+a(n-2)-2*a(n-3). 0
 0, 2, 11, 57, 292, 1495, 7653, 39176, 200543, 1026585, 5255116, 26901079, 137707341, 704927552, 3608542943, 18472227585, 94559825764, 484054270519, 2477886723189, 12684368234936, 64931619356831, 332386691572713 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Old name was: 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}}. Characteristic polynomial x^3-5*x^2-x+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). LINKS Table of n, a(n) for n=0..21. Index entries for linear recurrences with constant coefficients, signature (5, 1, -2). FORMULA a(n) = 5*a(n-1)+a(n-2)-2*a(n-3). G.f.: x*(2+x)/(1-5*x-x^2+2*x^3). - Colin Barker, May 02 2012 MATHEMATICA 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}] LinearRecurrence[{5, 1, -2}, {0, 2, 11}, 30] (* Harvey P. Dale, Sep 25 2017 *) CROSSREFS Sequence in context: A037490 A037570 A240888 * A164581 A054130 A037738 Adjacent sequences: A120461 A120462 A120463 * A120465 A120466 A120467 KEYWORD nonn,easy,changed AUTHOR Roger L. Bagula, Jul 01 2006 EXTENSIONS Edited by N. J. A. Sloane, Jul 13 2007 Better name by Colin Barker, May 02 2012 STATUS approved

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Last modified September 18 08:29 EDT 2024. Contains 375997 sequences. (Running on oeis4.)