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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
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.
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
Sequence in context: A054866 A242935 A109616 * A018262 A336542 A018356
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