OFFSET
0,2
COMMENTS
3-symbol substitution for the characteristic polynomial: x^3 - 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. Also at ResearchGate
FORMULA
a(n) = p(2*n), where p(n) maps the fixed point morphism 1 -> 3; 2 -> 1,2,2; 3 -> 1,2, starting with p(0) = 1.
EXAMPLE
The first few steps of the substitution are:
Start: 1
Maps:
1 --> 3
2 --> 1 2 2
3 --> 1 2
-------------
a(n) = p(2*n)
-------------
0: (#=1) (p(0))
1
1: (#=2) (p(2))
12
2: (#=9) (p(4))
123122122
3: (#=45) (p(6))
123122122312212312212231221221231221223122122
MATHEMATICA
s[1]= {3}; s[2]= {1, 2, 2}; s[3]= {1, 2}; t[b_]:= Flatten[s /@ b];
p[0]= {1}; p[1]= t[p[0]]; p[n_]:= t[p[n-1]];
a[n_]:= p[2*n];
a[4]
CROSSREFS
KEYWORD
nonn,less
AUTHOR
Roger L. Bagula, May 17 2005
EXTENSIONS
Edited by G. C. Greubel, Apr 03 2022
STATUS
approved