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A106798 Fixed point of the morphism 1 -> 3; 2 -> 1,2,2; 3 -> 1,2, starting with a(0) = 1.

%I A106798 #23 Apr 05 2022 03:25:43
%S A106798 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 A106798 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 A106798 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 A106798 Fixed point of the morphism 1 -> 3; 2 -> 1,2,2; 3 -> 1,2, starting with a(0) = 1.
%C A106798 3-symbol substitution for the characteristic polynomial: x^3 - 2*x^2 - x + 1.
%H A106798 G. C. Greubel, <a href="/A106798/b106798.txt">Table of n, a(n) for n = 0..10000</a>
%H A106798 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 A106798 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%F A106798 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 A106798 The first few steps of the substitution are:
%e A106798 Start: 1
%e A106798 Maps:
%e A106798   1 --> 3
%e A106798   2 --> 1 2 2
%e A106798   3 --> 1 2
%e A106798 -------------
%e A106798 a(n) = p(2*n)
%e A106798 -------------
%e A106798 0:   (#=1) (p(0))
%e A106798   1
%e A106798 1:   (#=2) (p(2))
%e A106798   12
%e A106798 2:   (#=9) (p(4))
%e A106798   123122122
%e A106798 3:   (#=45) (p(6))
%e A106798   123122122312212312212231221221231221223122122
%t A106798 s[1]= {3}; s[2]= {1,2,2}; s[3]= {1,2}; t[b_]:= Flatten[s /@ b];
%t A106798 p[0]= {1}; p[1]= t[p[0]]; p[n_]:= t[p[n-1]];
%t A106798 a[n_]:= p[2*n];
%t A106798 a[4]
%Y A106798 Cf. A106749, A106795, A106796, A106797.
%K A106798 nonn,less
%O A106798 0,2
%A A106798 _Roger L. Bagula_, May 17 2005
%E A106798 Edited by _G. C. Greubel_, Apr 03 2022