FIR filter : $h(n)$ is palindrome?
There are four types of linear phase FIR filters, as described in this answer. They have to satisfy the following symmetry conditions:

$$h[n]=h[N-1-n]\quad \text{or}\quad h[n]=-h[N-1-n]\tag{1}$$

(assuming the impulse response $h[n]$ is zero for $n&lt;0$ and $n\ge N$). Since your filter satisfies neither of the two conditions given by $(1)$ it can't have a linear phase response.