I have now implemented the "disklike polyomino" algorithm (as described in my previous message) and the automatically generated results agree with Allan's proposed sequence. I have verified A(6)=25 and A(7)=48 by visual inspection of the 35 hexominoes and 108 heptominoes. For N=1 through 13, my program computes: 1, 1, 2, 5, 10, 25, 48, 107, 193, 365, 621, 1082, 1715 I have submitted this sequence to OEIS as A181785 <http://oeis.org/A181785>. I have also created a web page for the sequence, which includes pictures of the "disklike" polyominoes for N=6 and N=7. On Sat, May 7, 2011 at 17:48, Robert Munafo <mrob27@gmail.com> wrote:
The way I interpreted the original question, based on Allan's description and his proposed sequence 1, 1, 2, 5, 10, 25 was:
Given a polyomino P on a square lattice, if you replace each of the squares in P with a point (say the "upper-left" corner) and call that set of points S, and then define H to be the convex hull of S, then the polyomino is said to be "disklike" if all lattice points in H are also in S.
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