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`%I #4 Dec 21 2020 07:24:45
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`%S 1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,
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`%T 1,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,1,
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`%U 1,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,1,1
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`%N Odd bisection of the infinite Fibonacci word A003849.
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`%F a(n) = 2 - [(2n+3)r] - [(2n+2)r], where [ ] = floor and r = golden ratio (A001622).
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`%e A003849 = (0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0,.. ), so that
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`%e A339824 = (0, 0, 1, 1, 0, 0, 1,...), the even bisection.
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`%e A339825 = (1, 0, 0, 0, 1, 0, 0,...), the odd bisection.
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`%t r = (1 + Sqrt[5])/2; z = 300;
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`%t f[n_] := 2 - Floor[(n + 2) r] + Floor[(n + 1) r]; (*A003849*)
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`%t Table[2 - Floor[(2 n + 2) r] + Floor[(2 n + 1) r], {n, 0, Floor[z/2]}] (*A339824 *)
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`%t Table[2 - Floor[(2 n + 3) r] + Floor[(2 n + 2) r], {n, 0, Floor[z/2]}] (*A339825 *)
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`%Y Cf. A001622, A096270, A339824, A339826, A339827.
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`%K nonn
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`%O 0
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`%A _Clark Kimberling_, Dec 19 2020
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