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A106795
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3-symbol substitution that has a real root cubic characteristic polynomial: x^3+9*x^2-3*x-1.
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0
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1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 2, 2, 3, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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COMMENTS
| The study of real root cubic Pisots by E. Bombieri and C. Frougny is related to the Penrose aperiodic tiling types. Roots hare are:{{x -> -0.20473}, {x -> 0.565376}, {x -> 8.63935}}
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REFERENCES
| Pure Discrete Spectrum for One Dimensional Substitution Systems of Pisot Type, V. F. Sirvent and B. Solomyak, page 14
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FORMULA
| 1->{1, 1, 1, 1, 1, 1, 2, 2, 3, 3}, 2->{2, 2, 3, 1, 1, 1, 1}, 3->{3, 1, 1, 1, 2, 2}
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MATHEMATICA
| s[1] = {1, 1, 1, 1, 1, 1, 2, 2, 2, 3}; s[2] = {2, 2, 3, 1, 1, 1, 1}; s[3] = {3, 1, 1, 1, 2, 2}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[2]
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CROSSREFS
| Cf. A106749.
Sequence in context: A004481 A004489 A112599 * A162203 A071455 A198862
Adjacent sequences: A106792 A106793 A106794 * A106796 A106797 A106798
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 17 2005
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