A339052 - OEIS

%I #17 Mar 29 2024 22:15:04

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

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

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

%N Odd bisection of the infinite Fibonacci word A096270.

%H A.H.M. Smeets, <a href="/A339052/b339052.txt">Table of n, a(n) for n = 0..20000</a>

%F a(n) = [(2n+2)r] - [(2n+1)r] - 1, where [ ] = floor and r = golden ratio (A001622).

%F a(n) = A005206(2*n+1) - A005206(2*n) = A001961(n+1) - A001965(n). - _Peter Bala_, Aug 09 2022

%e A096270 = (0,1,0,1,1,0,1,0,1,1,0,1,1,.. ), so that

%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, A001961, A001965, A005206, A096270, A339051, A339053, A339054.

%K nonn,easy

%O 0

%A _Clark Kimberling_, Dec 08 2020