The perimeter of a polyhex is always even. a(n) is partial sums of A057779(n) - Hexagonal polyominoes (or polyhexes, A000228) with perimeter 2n. a(2n+1) >= A131467(n) - Number of planar polyhexes (A000228) with at most n cells.
CROSSREFS
Cf. A038142 - Number of planar cata-polyhexes with n cells.