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A283318
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Image of 0 under repeated applications of the morphism 0 -> 0,1,0,0, 1 -> 1,1,0,1.
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2
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0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1
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REFERENCES
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Bernardino, André, Rui Pacheco, and Manuel Silva. "Coloring factors of substitutive infinite words." Discrete Mathematics 340.3 (2017): 443-451. See Example 3.
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LINKS
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FORMULA
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a(n) = a(4n) = a(4n-3).
a(4n-1) = 0.
a(4n-2) = 1.
G.f. g(x) satisfies g(x) = (1+1/x^3) g(x^4) + x^2/(1-x^4). (End)
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MAPLE
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with(ListTools);
psi:=proc(S)
Flatten(subs( {0=[0, 1, 0, 0], 1=[1, 1, 0, 1]}, S));
end;
S:=[0];
for n from 1 to 6 do S:=psi(S): od:
S;
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MATHEMATICA
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SubstitutionSystem[{0 -> {0, 1, 0, 0}, 1 -> {1, 1, 0, 1}}, {0}, 4] // Last (* Jean-François Alcover, Jan 21 2018 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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