Solve for $n$ : $\lfloor{(n+1)\phi}\rfloor x + ny < z$

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Solve for the biggest value of $n$ such that :

$$\lfloor{(n+1)\phi}\rfloor x + ny < z$$

where $n$ is a positive integer , and $x,y,z$ are known parameters.

This problem arised when solving a computational problem . I tried to solve it and even plug it into wolfram alpha but with fail.

I want to find the number of element less than $Z$ in a given column of a Wythoff Array . Is there any mathematical way to do it ?