A342963 a(n) is the number of sticky polyhexes with 2*n cells.

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

Offset: 1

Author

Woosuk Kwak, Mar 31 2021

Keywords

• nonn
• hard
• more

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.

Examples

			The two sticky tetrahexes are:
    * *    * * *
     * *    *
The following is the full list of 15 sticky hexahexes (polyhexes of size 6):
    * * *    * * *    *        * * * *    * * *
     * *      * *    * * * *    * *          * * *
      *          *        *
---
    * *       *        * *       * *     * * *
     * * *   * * * *    * * *   * * *       * *
        *       *      *         *         *
---
    * * *    * * *    * * * *   * * *    * * *
       * *    * * *    *   *       *        * *
          *                       * *        *
		

Links

• Woosuk Kwak, Sticky Polyhexes, Code Golf Stack Exchange.

Crossrefs

Cf. A000228.