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Triangle of trajectory of 1 under the morphism 1->2, 2->13, 3->1.
0

%I #11 Oct 02 2016 10:13:15

%S 1,1,2,1,2,2,1,3,1,2,2,1,3,2,1,3,1,3,2,1,1,2,2,1,3,2,1,3,1,3,2,1,2,1,

%T 3,1,3,2,1,1,3,2,1,2,1,1,3,2,1,2,2,1,3,2,1,3,1,3,2,1,2,1,3,1,3,2,1,1,

%U 3,2,1,2,1,1,3,2,2,1,3,1,3,2,1,1,3,2,1,2,1,1,3,2,1,3,2,1,2,1,1,3,2,2,1,1,3

%N Triangle of trajectory of 1 under the morphism 1->2, 2->13, 3->1.

%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

%e The first steps are:

%e {1}

%e {1, 2}

%e {1, 2, 2, 1, 3}

%e {1, 2, 2, 1, 3, 2, 1, 3, 1, 3, 2, 1}

%t s[1] = {2}; s[2] = {1, 3}; s[3] = {1}; t[a_] := Join[a, Flatten[s /@ a]]; p[0] = {1}; p[1] = t[{1}]; p[n_] := t[p[n - 1]] aa = Flatten[Table[p[n], {n, 0, 6}]]

%o (PARI) {a(n)=local(m, v, w); v=w=[1]; while(length(w)<n, m=length(v); for(k=1, m, v=concat(v, [[2],[1,3],[1]][v[k]])); w=concat(w, v)); w[n]}

%Y Cf. A073058, A105111.

%K nonn,tabf

%O 0,3

%A _Roger L. Bagula_, Apr 14 2005

%E Edited by the Associate Editors of the OEIS, Apr 07 2009