All sets of integer lattice points symmetric along the X and Y axes, and connected allowing diagonals, of size 14 and 15.
Code here: https://gist.github.com/mgritter/8cfc41a7325f85b75c029f77915a2f44
Inspired by this Quora question, https://www.quora.com/On-an-XY-array-of-lattice-points-how-many-patterns-of-N-connected-points-are-mirror-symmetric-in-both-X-and-Y-Adjacency-connections-are-1-in-X-1-in-Y-or-1-1-in-X-Y-I-do-not-know-the-answer, although I misinterpreted what he was asking for. That was closer to all polyominoes, allowing diagonal connections, which are horizontally and vertically symmetric. But I don't allow the line of symmetry to run down a half-integer value.
