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A181785
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Wechsler's "convex-hull polyominoes": convex hull contains no additional grid points.
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1
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1, 1, 2, 5, 10, 25, 48, 107, 193, 365, 621, 1082, 1715, 2777, 4247, 6519
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listen;
history;
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internal format)
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..16.
R. Munafo, Wechsler's Convex-Hull Polyominoes
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EXAMPLE
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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.
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CROSSREFS
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Cf. A000105
Sequence in context: A054866 A242935 A109616 * A018262 A336542 A018356
Adjacent sequences: A181782 A181783 A181784 * A181786 A181787 A181788
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KEYWORD
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nonn,hard
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AUTHOR
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Robert Munafo, May 08 2011
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EXTENSIONS
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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
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STATUS
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approved
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