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%I #23 Apr 05 2022 03:25:43
%S 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,
%T 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,
%U 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
%N Fixed point of the morphism 1 -> 3; 2 -> 1,2,2; 3 -> 1,2, starting with a(0) = 1.
%C 3-symbol substitution for the characteristic polynomial: x^3 - 2*x^2 - x + 1.
%H G. C. Greubel, <a href="/A106798/b106798.txt">Table of n, a(n) for n = 0..10000</a>
%H Victor F. Sirvent and Boris Solomyak, <a href="https://doi.org/10.4153/CMB-2002-062-3">Pure Discrete Spectrum for One-dimensional Substitution Systems of Pisot Type</a>. Canadian Mathematical Bulletin, 45(4), 2002, 697-710. Also at <a href="https://www.researchgate.net/publication/228561314_Pure_Discrete_Spectrum_for_One-dimensional_Substitution_Systems_of_Pisot_Type">ResearchGate</a>
%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%F 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.
%e The first few steps of the substitution are:
%e Start: 1
%e Maps:
%e 1 --> 3
%e 2 --> 1 2 2
%e 3 --> 1 2
%e -------------
%e a(n) = p(2*n)
%e -------------
%e 0: (#=1) (p(0))
%e 1
%e 1: (#=2) (p(2))
%e 12
%e 2: (#=9) (p(4))
%e 123122122
%e 3: (#=45) (p(6))
%e 123122122312212312212231221221231221223122122
%t s[1]= {3}; s[2]= {1,2,2}; s[3]= {1,2}; t[b_]:= Flatten[s /@ b];
%t p[0]= {1}; p[1]= t[p[0]]; p[n_]:= t[p[n-1]];
%t a[n_]:= p[2*n];
%t a[4]
%Y Cf. A106749, A106795, A106796, A106797.
%K nonn,less
%O 0,2
%A _Roger L. Bagula_, May 17 2005
%E Edited by _G. C. Greubel_, Apr 03 2022
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