How many subsets $P$ of $\{1, 2, ..., n\}$ are there such that if $x$ belongs to $P$ then $2x$ and $3x$ don't belong to $P$? For example, if $n = 4$ then there are $8$ such subsets (empty subset + $\{1\}$, $\{2\}$, $\{3\}$, $\{4\}$, $\{1, 4\}$, $\{2, 3\}$, $\{3, 4\}$
Specifically, I am asking for a formula for this sequence https://oeis.org/A050295