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 A106798 3-symbol substitution that has a real root cubic characteristic polynomial: x^3-2*x^2-x+1 : matrix isomer to Bombieri substitution. 0
 1, 2, 3, 1, 2, 2, 1, 2, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 2, 1, 2, 2, 3, 1, 2, 2, 1, 2, 2, 1, 2, 3, 1, 2, 2, 1, 2, 2, 3, 1, 2, 2, 1, 2, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 2, 1, 2, 2, 3, 1, 2, 2, 1, 2, 2, 1, 2, 3, 1, 2, 2, 1, 2, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 2, 1, 2, 2, 3, 1, 2, 2, 1, 2, 2, 1, 2, 3, 1, 2, 2, 1, 2, 2, 3, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The study of real root cubic Pisots by E. Bombieri and C. Frougny is related to the Penrose aperiodic tiling types. Roots here are:{{x -> -0.801938}, {x -> 0.554958}, {x -> 2.24698}} Matrix here has a block form: M={0,0,1},{1,2,0},{1,1,0}} Bonacci matrix equivalent is: M={0,1,0},{0,0,1},{-1,-1,2}} REFERENCES Pure Discrete Spectrum for One Dimensional Substitution Systems of Pisot Type, V. F. Sirvent and B. Solomyak, example 2, page 14 LINKS FORMULA 1->{3}, 2->{1, 2, 2}, 3->{1, 2} MATHEMATICA s[1] = {3}; s[2] = {1, 2, 2}; s[3] = {1, 2}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[8] CROSSREFS Cf. A106749. Sequence in context: A036848 A289585 A128864 * A214640 A224965 A194298 Adjacent sequences:  A106795 A106796 A106797 * A106799 A106800 A106801 KEYWORD nonn,uned AUTHOR Roger L. Bagula, May 17 2005 STATUS approved

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Last modified August 13 19:30 EDT 2020. Contains 336451 sequences. (Running on oeis4.)