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A277731
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Fixed point of the morphism 0 -> 01, 1 -> 012, 2 -> 0; starting with a(1) = 0.
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4
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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, 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, 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
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OFFSET
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1,5
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COMMENTS
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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).
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LINKS
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MAPLE
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with(ListTools);
T:=proc(S) Flatten(subs( {0=[0, 1], 1=[0, 1, 2], 2=[0]}, S)); end;
S:=[0];
for n from 1 to 10 do S:=T(S); od:
S;
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MATHEMATICA
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m = 100; (* number of terms required *)
S[1] = {0};
S[n_] := S[n] = SubstitutionSystem[{0 -> {0, 1}, 1 -> {0, 1, 2}, 2 -> {0}}, S[n-1]];
For[n = 2, True, n++, If[PadRight[S[n], m] == PadRight[S[n-1], m], Print["n = ", n]; Break[]]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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