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A277731 Fixed point of the morphism 0 -> 01, 1 -> 012, 2 -> 0; starting with a(1) = 0.

%I A277731 #17 Mar 20 2023 06:22:36
%S A277731 0,1,0,1,2,0,1,0,1,2,0,0,1,0,1,2,0,1,0,1,2,0,0,1,0,1,0,1,2,0,1,0,1,2,
%T A277731 0,0,1,0,1,2,0,1,0,1,2,0,0,1,0,1,0,1,2,0,1,0,1,2,0,1,0,1,2,0,0,1,0,1,
%U A277731 2,0,1,0,1,2,0,0,1,0,1,0,1,2,0,1,0,1,2,0,0,1,0,1,2
%N A277731 Fixed point of the morphism 0 -> 01, 1 -> 012, 2 -> 0; starting with a(1) = 0.
%C A277731 After k = 0,1,2,3,... applications of the morphism we have 0, 01, 01012, 01012010120, ... which have lengths 1, 2, 5, 11, 24, 53, 117, ..., satisfying b(n) = 2*b(n-1) + b(n-3) (cf. A052980).
%H A277731 N. J. A. Sloane, <a href="/A277731/b277731.txt">Table of n, a(n) for n = 1..20000</a>
%p A277731 with(ListTools);
%p A277731 T:=proc(S) Flatten(subs( {0=[0,1], 1=[0,1,2], 2=[0]}, S)); end;
%p A277731 S:=[0];
%p A277731 for n from 1 to 10 do S:=T(S); od:
%p A277731 S;
%t A277731 m = 100; (* number of terms required *)
%t A277731 S[1] = {0};
%t A277731 S[n_] := S[n] = SubstitutionSystem[{0 -> {0, 1}, 1 -> {0, 1, 2}, 2 -> {0}}, S[n-1]];
%t A277731 For[n = 2, True, n++, If[PadRight[S[n], m] == PadRight[S[n-1], m], Print["n = ", n]; Break[]]];
%t A277731 Take[S[n], m] (* _Jean-François Alcover_, Mar 20 2023 *)
%Y A277731 Cf. A052980, A277732, A277733, A277734.
%K A277731 nonn
%O A277731 1,5
%A A277731 _N. J. A. Sloane_, Nov 07 2016