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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A106788 Triangular three level substitution for chair tiling. 0 1, 1, 2, 3, 2, 3, 4, 4, 3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2, 3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2, 1, 1, 4, 3, 4, 3, 2, 2, 1, 1, 1, 1, 4, 4, 3, 2, 3, 2, 4, 3, 1 (list; graph; refs; listen; history; text; internal format) OFFSET 0,3 COMMENTS TriangularForm: {1, 1, 2, 3, 2, 3, 4, 4}, {3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2}, {3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2, 1, 1, 4, 3, 4, 3, 2, 2, 1, 1, 1, 1, 4, 4, 3, 2, 3, 2, 4, 3, 1, 1, 4, 3, 4, 3, 2, 2, 4, 3, 1, 4, 1, 4, 3, 3, 2, 2, 3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2, 1, 1, 4, 3, 4, 3, 2, 2, 1, 1, 1, 1, 4, 4, 3, 2, 3, 2, 4, 3, 1, 1, 4, 3, 4, 3, 2, 2, 4, 3, 1, 4, 1, 4, 3, 3, 2, 2}. REFERENCES Matching Rules and Substitution Tilings, Annals of Mathematics, 147 (1998), 181-223 by Chaim Goodman -Strauss (http://comp.uark.edu/~strauss/papers/index.html) LINKS Table of n, a(n) for n=0..104. FORMULA The substitution was derived by hand, one at a time. MATHEMATICA a[1] = {1, 1, 2, 3, 2, 3, 4, 4}; a[2] = {3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2}; a[3] = {3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2, 1, 1, 4, 3, 4, 3, 2, 2, 1, 1, 1, 1, 4, 4, 3, 2, 3, 2, 4, 3, 1, 1, 4, 3, 4, 3, 2, 2, 4, 3, 1, 4, 1, 4, 3, 3, 2, 2, 3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2, 1, 1, 4, 3, 4, 3, 2, 2, 1, 1, 1, 1, 4, 4, 3, 2, 3, 2, 4, 3, 1, 1, 4, 3, 4, 3, 2, 2, 4, 3, 1, 4, 1, 4, 3, 3, 2, 2} atable=Table[a[i], {i, 1.3}] MatrixForm[atable] aa = Table[a[i] /. 1 -> {1, 0} /. 2 -> {0, 1} /. 3 -> {-1, 0} /. 4 -> { 0, -1}, {i, 1, 3}] Table[ListPlot[FoldList[Plus, {0, 0}, aa[[i]]], PlotRange -> All, PlotJoined -> True, Axes -> False], {i, 1, 3}] CROSSREFS Sequence in context: A124524 A303543 A124525 * A123175 A143998 A054237 Adjacent sequences: A106785 A106786 A106787 * A106789 A106790 A106791 KEYWORD nonn AUTHOR Roger L. Bagula, May 16 2005 STATUS approved

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