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A181785 Wechsler's "convex-hull polyominoes": convex hull contains no additional grid points. 1

%I

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

%N Wechsler's "convex-hull polyominoes": convex hull contains no additional grid points.

%C 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.

%H R. Munafo, <a href="http://mrob.com/pub/math/seq-a181785.html">Wechsler's Convex-Hull Polyominoes</a>

%e For N=5 there are 12 polyominoes, but only 10 qualify. The two that do not are the "U" and "V" pentominoes, pictured here:

%e . * . * . . . * * *

%e . * * * . . . * . .

%e . . . . . . . * . .

%e 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.

%Y Cf. A000105

%K nonn,hard

%O 1,3

%A _Robert Munafo_, May 08 2011

%E Initial entry by _Robert Munafo_, May 08 2011

%E Name changed (with Wechsler's approval) by _Robert Munafo_, May 12 2011

%E a(14)-a(16) added by _Robert Munafo_, May 12 2011

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Last modified June 25 04:52 EDT 2021. Contains 345452 sequences. (Running on oeis4.)