A106054 Trajectory of 1 under the morphism 1->{2,2,1,2,2}, 2->{3}, 3->{4,4,3,4,4}, 4->{1}.

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

Offset

0,1

Comments

Pentasilver dragon 5-symbol substitution, characteristic polynomial x^4-2*x^3+x-16.

The existence of the three polynomials silver: x^4-2*x^3+x^2-4, double silver: x^4-4x^3+4x^2-4 and pentasilver: x^4-2*x^3+x-16 confirms that a Kenyon-like polynomial of a general form: x^4-p*x^3+q*x^2-r exists with substitutions associated to it.

Links

Table of n, a(n) for n=0..98.

Index entries for sequences that are fixed points of mappings

Mathematica

s[1] = {2, 2, 1, 2, 2}; s[2] = {3}; s[3] = {4, 4, 3, 4, 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: A224030 A233136 A339717 * A275437 A169695 A173642

Adjacent sequences: A106051 A106052 A106053 * A106055 A106056 A106057

Keyword

nonn

Author

Roger L. Bagula, May 06 2005

Extensions

Corrected and edited by N. J. A. Sloane, Jun 03 2005

Status

approved