A106052 Trajectory of 1 under the morphism 1->{2,1,1,2}, 2->{3}, 3->{4,3,3,4}, 4->{1}.

2, 1, 1, 2, 1, 4, 3, 3, 4, 4, 3, 3, 4, 1, 1, 4, 3, 3, 4, 4, 3, 3, 4, 1, 2, 1, 1, 2, 1, 4, 3, 3, 4, 4, 3, 3, 4, 1, 4, 3, 3, 4, 3, 2, 1, 1, 2, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 2, 1, 1, 2, 3, 4, 3, 3, 4, 4, 3, 3, 4, 3, 2, 1, 1, 2, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 2, 1, 1, 2, 3, 4, 3, 3, 4, 1, 4, 3, 3, 4, 4, 3, 3, 4, 1, 1

Offset

0,1

Comments

Double silver dragon 4-symbol substitution; characteristic polynomial x^4-4x^3+4x^2-4.

The existence of the two polynomials silver: x^4-2*x^3+x^2-4 and double silver: x^4-4x^3+4x^2-4 suggests that a Kenyon-like polynomial of a general form: x^4-p*x^3+q*x^2-r might exist with substitutions associated to it.

Links

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

Index entries for sequences that are fixed points of mappings

Mathematica

s[1] = {2, 1, 1, 2}; s[2] = {3}; s[3] = {4, 3, 3, 4}; s[4] = {1}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[5]

Crossrefs

Sequence in context: A053000 A002070 A326376 * A050473 A057593 A117008

Adjacent sequences: A106049 A106050 A106051 * A106053 A106054 A106055

Keyword

nonn

Author

Roger L. Bagula, May 06 2005

Status

approved