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A106798
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Fixed point of the morphism 1 -> 3; 2 -> 1,2,2; 3 -> 1,2, starting with a(0) = 1.
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4
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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, 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, 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
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OFFSET
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0,2
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COMMENTS
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3-symbol substitution for the characteristic polynomial: x^3 - 2*x^2 - x + 1.
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LINKS
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FORMULA
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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.
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EXAMPLE
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The first few steps of the substitution are:
Start: 1
Maps:
1 --> 3
2 --> 1 2 2
3 --> 1 2
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a(n) = p(2*n)
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0: (#=1) (p(0))
1
1: (#=2) (p(2))
12
2: (#=9) (p(4))
123122122
3: (#=45) (p(6))
123122122312212312212231221221231221223122122
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MATHEMATICA
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s[1]= {3}; s[2]= {1, 2, 2}; s[3]= {1, 2}; t[b_]:= Flatten[s /@ b];
p[0]= {1}; p[1]= t[p[0]]; p[n_]:= t[p[n-1]];
a[n_]:= p[2*n];
a[4]
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CROSSREFS
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KEYWORD
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nonn,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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