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A339824 Even bisection of the infinite Fibonacci word A003849. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 16 04:53 EDT 2021. Contains 343937 sequences. (Running on oeis4.)