A106038 Triangle Loop von Koch substitution: characteristic polynomial:x^3-6x^2+8*x.

1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 1, 3, 1, 2, 3, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 1, 3, 1, 2, 3, 1, 1, 2, 3, 1, 3, 1, 1, 3, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 1, 3, 1, 2, 3, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 2, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 1, 3, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 2, 3

Offset

0,2

Comments

To get the fractal: bb = aa /. 1 -> {1, 0} /. 2 -> {-1, N[Sqrt[3]]}/2 /. 3 -> {-1, -N[Sqrt[3]]}/2; ListPlot[FoldList[Plus, {0, 0}, bb], PlotJoined -> True, PlotRange -> All, Axes -> False];

Links

Table of n, a(n) for n=0..104.

Formula

1->{1, 2, 3, 1}, 2->{2, 1, 1, 2}, 3->{3, 1, 1, 3}

Mathematica

s[1] = {1, 2, 3, 1}; s[2] = {2, 1, 1, 2}; s[3] = {3, 1, 1, 3};; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[4]

Crossrefs

Sequence in context: A322874 A091654 A127246 * A078711 A338850 A322423

Adjacent sequences: A106035 A106036 A106037 * A106039 A106040 A106041

Keyword

nonn,uned

Author

Roger L. Bagula, May 05 2005

Status

approved