OFFSET
1,3
COMMENTS
These are polyominoes of the regular tiling with Schläfli symbol {6,3}. Each has a symmetry group of order 6. This sequence along with five others and A001207 can be used to determine A006535, the number of oriented polyominoes of the {6,3} regular tiling.
The sequence is calculated by using Redelmeier's method to generate fixed polyominoes, which are then mapped to one or two of the symmetric polyominoes as shown in the attachment.
LINKS
D. H. Redelmeier, Counting polyominoes: yet another attack, Discrete Math., 36 (1981), 191-203.
Robert A. Russell, Mapping fixed polyominoes
EXAMPLE
For a(1)=1, a(2)=1, and a(3)=2, the polyominoes are:
X X X X X X
X X X X X X X
X X X X X X X X X
X X X X X
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert A. Russell, Dec 21 2021
STATUS
approved