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A342963
a(n) is the number of sticky polyhexes of with 2*n cells.
0
1, 2, 15, 110, 1051, 10636, 113290, 1234189, 13674761, 153289285
OFFSET
1,2
COMMENTS
A sticky polyhex is defined as follows:
- A single dihex (polyhex of size 2) is a sticky polyhex.
- If a polyhex X is sticky, X plus a dihex Y is also sticky if X and Y share at least two unit sides.
- Any polyhex that cannot be formed by the above definition is not sticky.
This sequence counts free polyhexes; two polyhexes which are equivalent under reflection and/or rotation are counted only once.
a(n) < A000228(2n) for n > 1.
LINKS
Woosuk Kwak, Sticky Polyhexes, Code Golf Stack Exchange.
EXAMPLE
The two sticky tetrahexes are:
* * * * *
* * *
The following is the full list of 15 sticky hexahexes (polyhexes of size 6):
* * * * * * * * * * * * * *
* * * * * * * * * * * * *
* * *
---
* * * * * * * * * *
* * * * * * * * * * * * * * *
* * * * *
---
* * * * * * * * * * * * * * * *
* * * * * * * * * *
* * * *
CROSSREFS
Cf. A000228.
Sequence in context: A062808 A162773 A140637 * A022026 A026113 A052874
KEYWORD
nonn,hard,more
AUTHOR
Woosuk Kwak, Mar 31 2021
STATUS
approved