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%I #8 Jun 01 2017 10:15:33
%S 0,1,2,1,2,0,0,2,1,1,2,0,0,2,1,0,1,2,0,1,2,0,2,1,1,2,0,1,2,0,0,2,1,0,
%T 1,2,0,1,2,0,2,1,1,2,0,0,1,2,1,2,0,0,2,1,0,1,2,1,2,0,0,2,1,0,1,2,0,2,
%U 1,1,2,0,1,2,0,0,2,1,0,1,2,1,2,0,0,2
%N Start with 0 and repeatedly substitute 0->012, 1->120, 2->021.
%C This is the fixed point of the morphism 0->012, 1->120, 2->021 starting with 0. Let u be the (nonperiodic) sequence of positions of 0, and likewise, v for 1 and w for 2; then u(n)/n -> 3, v(n)/n -> 3, w(n)/n -> 3.
%C See A287385 for a guide to related sequences.
%H Clark Kimberling, <a href="/A287411/b287411.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%e First three iterations of the morphism: 012, 012120021, 012120021120021012012021120.
%t s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 2, 0}, 2->{0, 2, 1}}] &, {0}, 9]; (*A287411*)
%t Flatten[Position[s, 0]]; (*A287412*)
%t Flatten[Position[s, 1]]; (*A287413*)
%t Flatten[Position[s, 2]]; (*A287414*)
%Y Cf. A287385, A287412, A287413, A287414.
%K nonn,easy
%O 1,3
%A _Clark Kimberling_, May 25 2017
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