f(2n-1)=f(n)+f(n-1)+1

Solution for f(2n-1)=f(n)+f(n-1)+1 equation:

Simplifying
f(2n + -1) = f(n) + f(n + -1) + 1

Reorder the terms:
f(-1 + 2n) = f(n) + f(n + -1) + 1
(-1 * f + 2n * f) = f(n) + f(n + -1) + 1
(-1f + 2fn) = f(n) + f(n + -1) + 1

Multiply f * n
-1f + 2fn = fn + f(n + -1) + 1

Reorder the terms:
-1f + 2fn = fn + f(-1 + n) + 1
-1f + 2fn = fn + (-1 * f + n * f) + 1
-1f + 2fn = fn + (-1f + fn) + 1

Reorder the terms:
-1f + 2fn = 1 + -1f + fn + fn

Combine like terms: fn + fn = 2fn
-1f + 2fn = 1 + -1f + 2fn

Add 'f' to each side of the equation.
-1f + f + 2fn = 1 + -1f + f + 2fn

Combine like terms: -1f + f = 0
0 + 2fn = 1 + -1f + f + 2fn
2fn = 1 + -1f + f + 2fn

Combine like terms: -1f + f = 0
2fn = 1 + 0 + 2fn
2fn = 1 + 2fn

Add '-2fn' to each side of the equation.
2fn + -2fn = 1 + 2fn + -2fn

Combine like terms: 2fn + -2fn = 0
0 = 1 + 2fn + -2fn

Combine like terms: 2fn + -2fn = 0
0 = 1 + 0
0 = 1

Solving
0 = 1

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.