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A181785 Wechsler's "convex-hull 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 (list; graph; refs; listen; history; text; internal format)
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 "upper-left" 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 "convex-hull 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 Convex-Hull 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: A001431 A054866 A109616 * A018262 A018356 A026383

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

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Last modified March 24 21:58 EDT 2017. Contains 284001 sequences.