A320927 - OEIS

%I #4 Oct 25 2018 17:18:15

%S 0,0,0,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,1,

%T 0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,

%U 0,1,0,0,1,0,1,0,0,0,1,0,0,1,0,1,0,0

%N Concatenation of successive segments generated by the morphism {0 -> {0, 0, 1}, 1 -> {0,1,0}}, starting with 0.

%C Positions of 0: A320928

%C Positions of 1: A320929

%H Clark Kimberling, <a href="/A320927/b320927.txt">Table of n, a(n) for n = 1..20000</a>

%e First 4 segments:

%e {0},

%e {0, 0, 1},

%e {0, 0, 1, 0, 0, 1, 0, 1, 0},

%e {0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1}

%t s[n_] := Nest[Flatten[# /. {0 -> {0, 0, 1}, 1 -> {0, 1, 0}}] &, {0}, n];  (* A189628 *)

%t t = Table[s[n], {n, 0, 8}];  Take[t, 5]  (* successive segments of morphism s *)

%t u = Flatten[t]; Take[u, 200]                (* A320927 *)

%t v = Flatten[Position[u, 0]]; Take[v, 200]   (* A320928 *)

%t w = Flatten[Position[u, 1]];  Take[w, 200]  (* A320929 *)

%Y Cf. A189628, A320927, A320928, A320929.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Oct 24 2018