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A106154
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Generation 5 of the substitution 1->{2, 1, 2}, 2->{3, 2, 3}, 3->{4, 3, 4}, 4->{5, 4, 5}, 5->{6, 5, 6}, 6->{1, 6, 1}, starting with 1.
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1
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6, 5, 6, 5, 4, 5, 6, 5, 6, 5, 4, 5, 4, 3, 4, 5, 4, 5, 6, 5, 6, 5, 4, 5, 6, 5, 6, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 6, 5, 6, 5, 4, 5, 6, 5, 6, 5, 4, 5, 4, 3, 4, 5, 4, 5, 6, 5, 6, 5, 4, 5, 6, 5, 6, 5, 4, 5, 4, 3, 4
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OFFSET
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0,1
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COMMENTS
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Previous name was: Terdragon matrix symmetry extended to 6 symbols: characteristic polynomial: x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x - 63.
This sequence gives a segment of a 120-degree hexagonal border for a tile.
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LINKS
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F. M. Dekking, Recurrent Sets, Advances in Mathematics, vol. 44, no.1, April 1982, page 96, section 4.11.
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FORMULA
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1->{2, 1, 2}, 2->{3, 2, 3}, 3->{4, 3, 4}, 4->{5, 4, 5}, 5->{6, 5, 6}, 6->{1, 6, 1}.
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MATHEMATICA
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s[1] = {2, 1, 2}; s[2] = {3, 2, 3}; s[3] = {4, 3, 4}; s[4] = {5, 4, 5}; s[5] = {6, 5, 6}; s[6] = {1, 6, 1}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]]; aa = p[5]
Flatten[Nest[Flatten[#/.{1->{2, 1, 2}, 2->{3, 2, 3}, 3->{4, 3, 4}, 4->{5, 4, 5}, 5->{6, 5, 6}, 6->{1, 6, 1}} &], {5}, 7]] (* Vincenzo Librandi, Jun 17 2015 *)
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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