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%I #10 Apr 09 2019 15:11:40
%S 2,1,2,1,1,2,2,1,2,1,2,1,1,2,2,1,2,1,2,1,1,2,2,1,1,1,1,2,2,1,2,1,1,1,
%T 2,2,1,2,2,1,2,1,1,2,2,1,1,1,1,2,2,1,2,1,1,1,2,2,1,2,2,1,2,1,1,2,2,1,
%U 1,1,1,2,2,1,2,2,1,2,1,1,2,2,1,2,1,2,1,1,2,2,1,1,1,1,2,2,1,2,1,1,1,2,2,1,2
%N Trajectory of 2 under the morphism 1->{2, 1, 2, 1, 1, 2, 2, 1}, 2->{1, 1, 1, 2, 2, 1, 2}.
%D T. S. Blyth and E. F. Robertson, Essential Student Algebra: volume 5: Groups: Chapman and Hall, 1986, page 9.
%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%t s[1, 1] = {1}; s[2, 1] = {2};; s[1, 2] = {2}; s[2, 2] = {1};; s[1, 3] = {1, 2}; s[2, 3] = {1};; s[1, 4] = {1}; s[2, 4] = {1, 2};; s[1, 5] = {1, 2}; s[2, 5] = {2};; s[1, 6] = {2}; s[2, 6] = {1};; w[i_] = s[1, 1 + Mod[i, 6]] v[i_] = s[2, 1 + Mod[i, 6]] S[1] = Flatten[Table[w[i], {i, 1, 6}]] S[2] = Flatten[Table[v[i], {i, 1, 6}]] t[a_] := Flatten[S /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[3]
%t Nest[Flatten[#]/.{1->{2,1,2,1,1,2,2,1},2->{1,1,1,2,2,1,2}}&,2,4]//Flatten (* _Harvey P. Dale_, Apr 09 2019 *)
%Y Cf. A001030, A006338.
%K nonn
%O 0,1
%A _Roger L. Bagula_, May 17 2005
%E Edited by _N. J. A. Sloane_, Nov 12 2006
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