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A339052
Odd bisection of the infinite Fibonacci word A096270.
7
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, 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
OFFSET
0
LINKS
FORMULA
a(n) = [(2n+2)r] - [(2n+1)r] - 1, where [ ] = floor and r = golden ratio (A001622).
a(n) = A005206(2*n+1) - A005206(2*n) = A001961(n+1) - A001965(n). - Peter Bala, Aug 09 2022
EXAMPLE
A096270 = (0,1,0,1,1,0,1,0,1,1,0,1,1,.. ), so that
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*)
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Dec 08 2020
STATUS
approved