Description of A007413 as the rows of a triangle:
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 02 2008

%I A007413
%S A007413 1, 1,2,3, 1,2,3,1,3,2, 1,2,3,1,3,2,1,2,3,2,1,3, 
1,2,3,1,3,2,1,2,3,2,1,3,1,2,3,1,3,2,1,3,1,2,3,2, 
1,2,3,1,3,2,1,2,3,2,1,3,1,2,3,1,3,2,1,3,1,2,3,2,1,2,3,1,3,2,1,2,3,2,1,3,1,2,3,
2,1,2,3,1,3,2,1,3
%N A007413 The characteristic polynomial of the graph matrix is -x^3+x^2+2*x
%C A007413 These sequences as triangular forms have lengths 
like the Pc Mandelbrot-Julia polynomial;
that fact suggests that the levels might be projected as coefficient polynomials.
That presents an whole new way of seeing substitution sequences:
1,
1+2*x+3*x^2
1+2*x+3*x^2+x^3+3x^3+2*x^5
etc.
Which can be projected to the complex plane as:
x->a+i*b
and plotted implicitly.
%D A007413  A. Thue. Ueber unendliche Zeichenreihe. Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiania, 7:1a22, 1906.
%D A007413 http://south.rotol.ramk.fi/keranen/ias2002/NewAbelianSquare-FreeDT0L-LanguagesOver4Letters.nb
%F A007413 M=
{{1, 1, 1}, 
{1, 0, 1}, 
{0, 1, 0}}.
%e A007413 Triangular sequence form:
{1},        
{1,2,3},       
{1,2,3,1,3,2},
{1,2,3,1,3,2,1,2,3,2,1,3},
{1,2,3,1,3,2,1,2,3,2,1,3,1,2,3,1,3,2,1,3,1,2,3,2},
{1,2,3,1,3,2,1,2,3,2,1,3,1,2,3,1,3,2,1,3,1,2,3,2,1,2,3,1,3,2,1,2,3,2,1,3,1,2,3,2,1,2,3,1,3,2,1,3}
%t A007413 Clear[productions, a]
productions = {"1" -> "1,2,3", "2" -> "1,3", "3" -> "2", " " -> ""};;
g[x_] := StringReplace[x, productions]
a = NestList[g, "1", 5]
%Y A007413 Cf. A001285