%I #4 Mar 30 2012 17:34:15
%S 1,1,1,1,3,3,7,7,9,1,1,1,1,3,3,7,7,9,1,1,1,1,3,3,7,7,9,1,1,1,1,3,3,7,
%T 7,9,2,2,8,2,2,8,4,4,6,4,4,6,5,1,1,1,1,3,3,7,7,9,1,1,1,1,3,3,7,7,9,1,
%U 1,1,1,3,3,7,7,9,1,1,1,1,3,3,7,7,9,2,2,8,2,2,8,4,4,6,4,4,6,5,1,1,1,1,3,3,7
%N Bombieri matrix self-similar doubling to 9 symbols in substitution.
%C Characteristic polynomial is -x^9+4*x^8+10*x^10-21*x^6-21*x^5+35*x^4+7*x^3-12*x^2-x+1. Roots are ( eight real roots, three are duplicates): {{x -> -1.80194}, {x -> -1.80194}, { x -> -0.445042}, {x -> -0.445042}, {x -> 0.307979}, {x -> 0.643104}, { x -> 1.24698}, {x -> 1.24698}, {x -> 5.04892}}.
%F 1-> {1, 1, 1, 1, 3, 3, 7, 7, 9}; 2-> {1, 1, 3, 3, 7, 9}; 3-> {2, 2, 8}; 4-> {1, 1, 3, 7, 7, 9}; 5-> {1, 3, 7, 9}; 6-> {2, 8}; 7-> {4, 4, 6}; 8-> {4, 6}; 9-> {5};
%e Matrix is:
%e {{4, 0, 2, 0, 0, 0, 2, 0, 1},
%e {2, 0, 2, 0, 0, 0, 1, 0, 1},
%e {0, 2, 0, 0, 0, 0, 0, 1, 0},
%e {2, 0, 1, 0, 0, 0, 2, 0, 1},
%e {1, 0, 1, 0, 0, 0, 1, 0, 1},
%e {0, 1, 0, 0, 0, 0, 0, 1, 0},
%e {0, 0, 0, 2, 0, 1, 0, 0, 0},
%e {0, 0, 0, 1, 0, 1, 0, 0, 0},
%e {0, 0, 0, 0, 1, 0, 0, 0, 0}}
%t s[1] = {1, 1, 1, 1, 3, 3, 7, 7, 9}; s[2] = {1, 1, 3, 3, 7, 9}; s[3] = {2, 2, 8}; s[4] = {1, 1, 3, 7, 7, 9}; s[5] = {1, 3, 7, 9}; s[6] = {2, 8}; s[7] = {4, 4, 6}; s[8] = {4, 6}; s[9] = {5}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[3]
%K nonn,uned
%O 0,5
%A _Roger L. Bagula_, May 27 2005