A305397 Let k be the maximal number of vertices in an n X n lattice grid that form a convex polygon, then a(n) = floor(k/2).

2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 8, 9, 10, 10, 10, 11, 12

Offset: 1

Author

N. J. A. Sloane, Jun 27 2018

Keywords

• nonn
• more

Examples

			In a 3x3 square cells grid (which is rather 4x4 in the terms of vertices), one can choose eight vertices forming a convex octagon (namely, all non-corner boundary vertices) but no nine vertices to form a convex nonagon, therefore a(3) = floor(8/2) = 4, the "edge-diameter" of the octagon.
		

Links

• Antoine Deza, George Manoussakis, Shmuel Onn, Primitive Zonotopes, Discrete & Computational Geometry, 60 (No. 1, 2018), 40-56; arXiv preprint arXiv:1512.08018 [math.OC], 2015-2017. See Table 1.

Crossrefs

Cf. A011755, A049696, A374975.

Formula

a(A011755(n)) = A049696(n). [Deza et al., Proposition 3.1] - Andrey Zabolotskiy, Sep 27 2024

Extensions

Name clarified by Andrey Zabolotskiy, Sep 27 2024