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A106795 3-symbol substitution that has a real root cubic characteristic polynomial: x^3+9*x^2-3*x-1. 0
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; text; internal format)
OFFSET

0,7

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}}

REFERENCES

Pure Discrete Spectrum for One Dimensional Substitution Systems of Pisot Type, V. F. Sirvent and B. Solomyak, page 14

LINKS

Table of n, a(n) for n=0..86.

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}

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]

CROSSREFS

Cf. A106749.

Sequence in context: A307299 A307298 A216674 * A162203 A071455 A288724

Adjacent sequences:  A106792 A106793 A106794 * A106796 A106797 A106798

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, May 17 2005

STATUS

approved

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Last modified October 15 05:40 EDT 2019. Contains 328026 sequences. (Running on oeis4.)