login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=0..104.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 24 18:12 EDT 2019. Contains 326295 sequences. (Running on oeis4.)