A339824 Even bisection of the infinite Fibonacci word A003849.

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

Offset

0

Links

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

Formula

a(n) = 2 - [(2n+2)r] + [(2n+1)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, and
A339825 = (1, 0, 0, 0, 1, 0, 0, ...), the odd bisection.

Mathematica

r = (1 + Sqrt[5])/2; z = 300;
f[n_] := 2 - Floor[(n + 2) r] + Floor[(n + 1) r];  (* A003849 *)
Table[2 - Floor[(2 n + 2) r] + Floor[(2 n + 1) r], {n, 0, Floor[z/2]}](* A339824 *)
Table[2 - Floor[(2 n + 3) r] + Floor[(2 n + 2) r], {n, 0, Floor[z/2]}](* A339825 *)

Crossrefs

Cf. A001622, A096270, A339825, A339826, A339827.

Sequence in context: A285031 A327222 A286063 * A278587 A188257 A132380

Adjacent sequences: A339821 A339822 A339823 * A339825 A339826 A339827

Keyword

nonn

Author

Clark Kimberling, Dec 19 2020

Extensions

Corrected by Michel Dekking, Feb 23 2021

Status

approved