A106705 8-symbol substitution from X[n] Coxeter diagram with n=4.

1, 1, 7, 7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 7, 7, 7, 7, 7, 7, 7, 7, 1, 2, 3, 1, 2

Offset

0,3

Comments

Characteristic Polynomial n=4: x8-20*x6+128*x4-320*x2+256 This Coxeter diagram behaves very much like odd even blocks or branches. This program shows the triangular nature of the output.

References

X[n] substitutions of the Coxeter diagram from the McMullen article.

Curtis McMullen, Prym varieties and Teichmueller curves, May 04, 2005

Links

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

Formula

1->{7}*n, 2->{5.6, 7}, 3->{6, 7, 8}, 4->{6}*n, 5->{2}*n, 6->{2, 3, 4}, 7->{1, 2, 3}, 8->{3}*n

Mathematica

n0=8; n=4; s[1] = Table[If[i <= n0, 7, {}], {i, 1, n0}]; s[2] = {5, 6, 7}; s[ 3] = {6, 7, 8}; s[4] = Table[If[i <= n, 6, {}], {i, 1, n0}]; s[5] = Table[If[i <= n, 2, {}], {i, 1, n0}]; s[6] = {2, 3, 4}; s[7] = {1, 2, 3}; s[8] = Table[If[i <= n, 3, {}], {i, 1, n0}]; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = Flatten[Table[p[n], {n, 0, 3}]]

Crossrefs

Sequence in context: A269349 A112114 A031182 * A010727 A186684 A255910

Adjacent sequences: A106702 A106703 A106704 * A106706 A106707 A106708

Keyword

nonn,uned

Author

Roger L. Bagula, May 09 2005

Status

approved