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

1,5

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).

Links

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

Example

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

Crossrefs

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

Sequence in context: A086336 A237258 A108796 * A048849 A076211 A167186

Adjacent sequences: A364681 A364682 A364683 * A364685 A364686 A364687

Keyword

nonn

Author

Robert A. Russell, Aug 02 2023

Status

approved