A339825 - OEIS

A339825

Odd bisection of the infinite Fibonacci word A003849.

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, 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, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1

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OFFSET

LINKS

Table of n, a(n) for n=0..85.

FORMULA

a(n) = 2 - [(2n+3)r] - [(2n+2)r], where [ ] = floor and r = golden ratio (A001622).

EXAMPLE

A003849 = (0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0,.. ), so that

A339824 = (0, 0, 1, 1, 0, 0, 1,...), the even bisection.

A339825 = (1, 0, 0, 0, 1, 0, 0,...), the odd bisection.

MATHEMATICA

r = (1 + Sqrt[5])/2; z = 300;