  A set $E \subset \mathbb{N}$ is an interpolation set for nilsequences if
every bounded function on $E$ can be extended to a nilsequence on $\mathbb{N}$.
Following a theorem of Strzelecki, every lacunary set is an interpolation set
for nilsequences. We show that sublacunary sets are not interpolation sets for
nilsequences. Furthermore, we prove that the union of an interpolation set for
nilsequences and a finite set is an interpolation set for nilsequences. Lastly,
we provide a new class of interpolation sets for Bohr almost periodic
sequences, and as the result, obtain a new example of interpolation set for
$2$-step nilsequences which is not an interpolation set for Bohr almost
periodic sequences.
