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%I #14 Mar 29 2024 22:15:08
%S 0,0,1,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,0,0,1,1,
%T 0,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,
%U 0,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,0
%N Even bisection of the infinite Fibonacci word A096270.
%H A.H.M. Smeets, <a href="/A339051/b339051.txt">Table of n, a(n) for n = 0..20000</a>
%F a(n) = [(2n+1)r] - [2nr] - 1, where [ ] = floor and r = golden ratio (A001622).
%e A096270 = (0,1,0,1,1,0,1,0,1,1,0,1,1,...), so
%e A339051 = (0,0,1,1,1,0,...), the even bisection.
%e A339052 = (1,1,0,0,1,1,...), the odd bisection.
%t r = (1 + Sqrt[5])/2; z = 200;
%t Table[Floor[(2 n + 1) r] - Floor[2 n r] - 1, {n, 0, Floor[z/2]}] (* A339051 *)
%t Table[Floor[(2 n + 2) r] - Floor[(2 n + 1) r] - 1, {n, 0, Floor[z/2]}] (* A339052 *)
%Y Cf. A001622, A096270, A339052, A339053, A339054.
%K nonn,easy
%O 0
%A _Clark Kimberling_, Dec 08 2020
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