I've started looking at this, but still haven't got it generating the basic sequence A000105 correctly. I am getting: 1, 1, 1, 2, 5, 12, 35, 108, 368, 1280, ... (the 368 should be 369 and the 1280 should be 1285) Is there a database of polyominoes somewhere in text format so I can figure out which of the 369 I am missing? - Robert Munafo On Thu, May 5, 2011 at 18:35, Allan Wechsler <acwacw@gmail.com> wrote:

On a previous occasion, I talked about enumerating "disklike" polyominoes, polyominoes which occurred as the intersection between a disk and a square lattice. Today I tried counting polyominoes which occurred as the intersection between any convex figure and the lattice. This implies that the convex hull of the polyomino (viewed as a set of lattice points) includes no additional lattice points.

I call these polyominoes "convex", but apparently the term has already been taken by a different class, so I don't know what we should really call them.

Starting from the monomino, the counts seem to be 1, 1, 2, 5, 10, 25. The sequence is not in OEIS, though I confess some uncertainty about the 25 convex hexominoes, and would like confirmation.

-- Robert Munafo -- mrob.com Follow me at: fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com- youtube.com/user/mrob143 - rilybot.blogspot.com