

A181785


Wechsler's "convexhull polyominoes": convex hull contains no additional grid points.


1



1, 1, 2, 5, 10, 25, 48, 107, 193, 365, 621, 1082, 1715, 2777, 4247, 6519
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OFFSET

1,3


COMMENTS

Given a polyomino P on a square lattice, if you replace each of the squares in P with a point (say the "upperleft" corner) and call that set of points S, then define H to be the convex hull of S: the polyomino is said to be a "convexhull polyomino" if all lattice points in H are also in S.


LINKS

Table of n, a(n) for n=1..16.
R. Munafo, Wechsler's ConvexHull Polyominoes


EXAMPLE

For N=5 there are 12 polyominoes, but only 10 qualify. The two that do not are the "U" and "V" pentominoes, pictured here:
. * . * . . . * * *
. * * * . . . * . .
. . . . . . . * . .
Both are "concave" in the sense that a convex hull of the 5 points in the pentomino also includes one grid point that is not in the pentomino.


CROSSREFS

Cf. A000105
Sequence in context: A054866 A242935 A109616 * A018262 A336542 A018356
Adjacent sequences: A181782 A181783 A181784 * A181786 A181787 A181788


KEYWORD

nonn,hard


AUTHOR

Robert Munafo, May 08 2011


EXTENSIONS

Initial entry by Robert Munafo, May 08 2011
Name changed (with Wechsler's approval) by Robert Munafo, May 12 2011
a(14)a(16) added by Robert Munafo, May 12 2011


STATUS

approved



