How can I prove that the fraction
$$P(n) = \frac{1}{60} (7 * 4^n - 42 * (-1)^n - 10) $$
is integer for all natural numbers by mathematical induction method?
I tried to find the difference between $P(k + 1)$ and $P(k)$, but could not transform it to the original fraction.
$$P(1)=\frac{1}{60}\left(28+42-10\right)=1$$ $$P(2)=\frac{1}{60}\left(112-42-10\right)=1$$ $$P(k+2)-P(k)=\frac{4^k\times 105}{60}=7\times4^{k-1}$$