A350700 a(n) is the number of 1's minus the number of 0's in A004685(n).

-1, 1, 1, 0, 2, 1, -2, 2, 1, -2, 4, 1, -4, 2, 3, -2, 6, 3, -4, -3, 3, -2, 1, 7, -4, -5, 1, 4, 3, 5, -4, 1, -4, 4, 1, -2, 0, 3, -6, -2, 5, 6, 0, 3, 6, -1, 11, -6, -9, 3, 2, -1, -1, -2, -5, 6, 4, -7, 8, 0, -9, -4, 10, 3, -4, 6, -7, 6, -17, -1, -2, -5, 1, 4, -3

Offset: 0

Author

Karl-Heinz Hofmann, Jan 18 2022

Keywords

• sign
• base

Examples

			A004685(0) = 0; this term has 0 ones and 1 zero. So a(0) = 0 - 1 = -1.
A004685(7) = 1101; this term has 3 ones and 1 zero. So a(7) = 3 - 1 = 2.
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000045, A004685, A011373, A145037, A177718, A214852.

Programs

Mathematica

a[n_] := Subtract @@ DigitCount[Fibonacci[n], 2, {1, 0}]; Array[a, 75, 0] (* Amiram Eldar, Jan 22 2022 *)

Python

from sympy import fibonacci
print([(bin(fibonacci(n))[2:].count("1") - bin(fibonacci(n))[2:].count("0")) for n in range (0,100)])

Formula

a(n) = A145037(A000045(n)) for n >= 1.

a(n) = 0 if and only if n is in A214852. - Amiram Eldar, Jan 22 2022