OFFSET
0,7
COMMENTS
3-symbol substitution for the characteristic polynomial: x^3 + 9*x^2 - 3*x - 1.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Victor F. Sirvent and Boris Solomyak, Pure Discrete Spectrum for One-dimensional Substitution Systems of Pisot Type. Canadian Mathematical Bulletin, 45(4), 2002, 697-710; (page 708 example 3). Also at ResearchGate
EXAMPLE
The first few steps of the substitution are:
Start: 1
Maps:
1 --> 1 1 1 1 1 1 2 2 2 3
2 --> 2 2 3 1 1 1 1
3 --> 3 1 1 1 2 2
-------------
0: (#=1)
1
1: (#=10)
1111112223
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]]; p[3]
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, May 17 2005
EXTENSIONS
Edited by G. C. Greubel, Apr 03 2022
STATUS
approved