Polyhexes with holes: A038144 and A057210

[Joseph S. Myers]

Are A038144 and A057210 duplicates?  If not, what does the definition of
A038144 mean?

Both sequences count the some form of the number of polyhexes with holes.
A057210 counts (planar) polyhexes (in the usual sense, i.e. that of
A000228) with holes; has author Warren Power (wjpnply(AT)hotmail.com), Sep
27 2000; and had terms 0,0,0,0,0,1,2,13,67,404,2323 (with a reference to a
tangentially related web page of mine) until I added some more terms as an
extension last year.  A038144 is more obscure; the description is
"Hexagonal planar circulenes (planar rings of hexagons) with n cells."; it
has fewer terms listed (0,0,0,0,0,1,2,13,67,404) and a reference to J. V.
Knop et al., On the total number of polyhexes, Match, No. 16 (1984),
119-134.

Reading that referenced paper still leaves the meaning of A038144 obscure
(to me), apparently presuming some background in what are counted as valid
"chemical" (not necessarily planar) polyhexes.  The paper says "... the
number of planar mono-circulenes [footnote: Di-circulenes do not appear in
benzenoid hydrocarbons with less than 15 hexagons].  These are given in
Table 5.".  Table 5, which has the sequence terms 1,2,13,67,404 in it, is
headed "The number of hexagonal planar circulenes, i.e. planar rings of
hexagons" while the relevant column is headed "Number of planar
mono-circulenes".

So the question here is what exactly is meant by "planar mono-circulenes"
and "di-circulenes" and thus whether A038144 is or is not the same as
A057210.

Some other sequences relating to "chemical" polyhexes could do with better
explanations of exactly what configurations are allowed, e.g. A038147,
"Polyhexes with n cells." (same paper referenced).

-- 
Joseph S. Myers
jsm28 at cam.ac.uk