A364684 Number of achiral triangular polyominoes with 6n cells and sixfold rotational symmetry.

1, 1, 1, 1, 3, 4, 7, 9, 16, 22, 46, 63, 121, 167, 455, 912, 1263, 2535, 3514, 7099, 9873, 20043, 27956, 56807, 79397, 161736, 226559, 462482, 649100, 1327165, 1865833, 3820605, 5379507, 11028753, 15550459, 31913892, 45057416, 92557088, 130837407, 268988726

Offset: 1

Author

Robert A. Russell, Aug 02 2023

Keywords

• nonn

Comments

These are polyominoes of the regular tiling with Schläfli symbol {3,6}. Their center is a vertex. As their symmetry group of order 12 is maximal, we can consider them either fixed, oriented (one-sided), or unoriented (free).

Examples

			                            ________          ________
                /\         /\  /\  /\        /\  /\  /\
    ____   ____/__\____   /__\/__\/__\      /__\/__\/__\
   /\  /\  \  /\  /\  /  /\  /    \  /\    /\  /\  /\  /\
  /__\/__\  \/__\/__\/  /__\/      \/__\  /__\/__\/__\/__\
  \  /\  /  /\  /\  /\  \  /\      /\  /  \  /\  /\  /\  /
   \/__\/  /__\/__\/__\  \/__\____/__\/    \/__\/__\/__\/
               \  /       \  /\  /\  /      \  /\  /\  /
                \/         \/__\/__\/        \/__\/__\/
		

Links

• Robert A. Russell, Table of n, a(n) for n = 1..53

Crossrefs

Cf. A006534 (oriented), A000577 (unoriented), A030224 (chiral), A030223 (achiral), A001420 (fixed).