OFFSET
0,3
COMMENTS
4-symbol substitution for the Pisot characteristic polynomial: x^4 - 2*x^2 - 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 709 example 3). Also at ResearchGate
EXAMPLE
The first few steps of the substitution are:
Start: 1
Maps:
1 --> 1 1 2
2 --> 3
3 --> 1 4
4 --> 1
-------------
0: (#=1)
1
1: (#=3)
112
2: (#=7)
1121123
3: (#=16)
1121123112112314
4: (#=36)
112112311211231411211231121123141121
5: (#=82)
1121123112112314112112311211231411211121123112112314112112311211231411211121123112
MATHEMATICA
s[1]= {1, 1, 2}; s[2]= {3}; s[3]= {1, 4}; s[4]= {1}; t[b_]:= Flatten[s /@ b];
a[0]= {1}; a[1]= t[p[0]]; a[n_]:= t[a[n-1]];
a[10]
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, May 17 2005
EXTENSIONS
Edited by G. C. Greubel, Apr 03 2022
STATUS
approved