%I #16 Apr 20 2021 10:08:26

%S 1,2,15,110,1051,10636,113290,1234189,13674761,153289285

%N a(n) is the number of sticky polyhexes of with 2*n cells.

%C A sticky polyhex is defined as follows:

%C - A single dihex (polyhex of size 2) is a sticky polyhex.

%C - If a polyhex X is sticky, X plus a dihex Y is also sticky if X and Y share at least two unit sides.

%C - Any polyhex that cannot be formed by the above definition is not sticky.

%C This sequence counts free polyhexes; two polyhexes which are equivalent under reflection and/or rotation are counted only once.

%C a(n) < A000228(2n) for n > 1.

%H Woosuk Kwak, <a href="https://codegolf.stackexchange.com/questions/222709/sticky-polyhexes">Sticky Polyhexes</a>, Code Golf Stack Exchange.

%e The two sticky tetrahexes are:

%e * * * * *

%e * * *

%e The following is the full list of 15 sticky hexahexes (polyhexes of size 6):

%e * * * * * * * * * * * * * *

%e * * * * * * * * * * * * *

%e * * *

%e ---

%e * * * * * * * * * *

%e * * * * * * * * * * * * * * *

%e * * * * *

%e ---

%e * * * * * * * * * * * * * * * *

%e * * * * * * * * * *

%e * * * *

%Y Cf. A000228.

%K nonn,hard,more

%O 1,2

%A _Woosuk Kwak_, Mar 31 2021