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A339051
Even bisection of the infinite Fibonacci word A096270.
7
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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Dec 08 2020
STATUS
approved