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%I #24 Apr 05 2022 03:26:32
%S 1,1,2,1,1,2,3,1,1,2,1,1,2,3,1,4,1,1,2,1,1,2,3,1,1,2,1,1,2,3,1,4,1,1,
%T 2,1,1,1,2,1,1,2,3,1,1,2,1,1,2,3,1,4,1,1,2,1,1,2,3,1,1,2,1,1,2,3,1,4,
%U 1,1,2,1,1,1,2,1,1,2,3,1,1,2,1,1,2,1,1,2,3,1,1,2,1,1,2,3,1,4,1,1,2,1,1,2,3
%N Fixed point of the morphism 1 -> 1,1,2; 2 -> 3; 3 -> 1,4; 4 -> 1, starting with a(0) = 1.
%C 4-symbol substitution for the Pisot characteristic polynomial: x^4 - 2*x^2 - x - 1.
%H G. C. Greubel, <a href="/A106796/b106796.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; (page 709 example 3). 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>
%e The first few steps of the substitution are:
%e Start: 1
%e Maps:
%e 1 --> 1 1 2
%e 2 --> 3
%e 3 --> 1 4
%e 4 --> 1
%e -------------
%e 0: (#=1)
%e 1
%e 1: (#=3)
%e 112
%e 2: (#=7)
%e 1121123
%e 3: (#=16)
%e 1121123112112314
%e 4: (#=36)
%e 112112311211231411211231121123141121
%e 5: (#=82)
%e 1121123112112314112112311211231411211121123112112314112112311211231411211121123112
%t s[1]= {1, 1, 2}; s[2]= {3}; s[3]= {1, 4}; s[4]= {1}; t[b_]:= Flatten[s /@ b];
%t a[0]= {1}; a[1]= t[p[0]]; a[n_]:= t[a[n-1]];
%t a[10]
%Y Cf. A106749, A106795, A106797, A106798.
%K nonn
%O 0,3
%A _Roger L. Bagula_, May 17 2005
%E Edited by _G. C. Greubel_, Apr 03 2022
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