This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A305397 #14 Sep 27 2024 23:15:39 %S A305397 2,3,4,4,5,6,6,7,8,8,8,9,10,10,10,11,12 %N 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). %H A305397 Antoine Deza, George Manoussakis, Shmuel Onn, <a href="https://doi.org/10.1007/s00454-017-9873-z">Primitive Zonotopes</a>, Discrete & Computational Geometry, 60 (No. 1, 2018), 40-56; <a href="https://arxiv.org/abs/1512.08018">arXiv preprint</a> arXiv:1512.08018 [math.OC], 2015-2017. See Table 1. %F A305397 a(A011755(n)) = A049696(n). [Deza et al., Proposition 3.1] - _Andrey Zabolotskiy_, Sep 27 2024 %e A305397 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. %Y A305397 Cf. A011755, A049696, A374975. %K A305397 nonn,more %O A305397 1,1 %A A305397 _N. J. A. Sloane_, Jun 27 2018 %E A305397 Name clarified by _Andrey Zabolotskiy_, Sep 27 2024