A339051 Even bisection of the infinite Fibonacci word A096270.

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

Offset

0

Links

A.H.M. Smeets, Table of n, a(n) for n = 0..20000

Formula

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

Example

A096270 = (0,1,0,1,1,0,1,0,1,1,0,1,1,...), so
A339051 = (0,0,1,1,1,0,...), the even bisection.
A339052 = (1,1,0,0,1,1,...), the odd bisection.

Mathematica

r = (1 + Sqrt[5])/2; z = 200;
Table[Floor[(2 n + 1) r] - Floor[2 n r] - 1, {n, 0, Floor[z/2]}] (* A339051 *)
Table[Floor[(2 n + 2) r] - Floor[(2 n + 1) r] - 1, {n, 0, Floor[z/2]}] (* A339052 *)

Crossrefs

Cf. A001622, A096270, A339052, A339053, A339054.

Sequence in context: A359606 A072126 A287125 * A234045 A238468 A111113

Adjacent sequences: A339048 A339049 A339050 * A339052 A339053 A339054

Keyword

nonn,easy

Author

Clark Kimberling, Dec 08 2020

Status

approved