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 A298562 #52 Oct 02 2023 16:46:50 %S A298562 4,6,6,6,8,7,8,9,8,8,10,9,9,10,10,10,10,11,11,12,12,12,11,11,12,12,12, %T A298562 13,12,12,13,13,13,13,14,14,13,13,14,14,14,14,14,14,14,15,14,15,15,15, %U A298562 15,15,16,15,16,15,16,16,15,15,16,16,16,16,16,16,16,16,17,17,16,17,17,17,17,17 %N A298562 Quantitative (polygonal) Helly numbers for the integer lattice Z^2. %C A298562 a(n) = g(Z^2,n) is the maximum integer k > 0 such that there exists a lattice polygon with k vertices containing exactly n+k lattice points (in its interior or on the boundary). [edited by _Günter Rote_, Oct 01 2023] %H A298562 Günter Rote, <a href="/A298562/b298562.txt">Table of n, a(n) for n = 0..200</a> %H A298562 G. Averkov, B. González Merino, I. Paschke, M. Schymura, and S. Weltge, <a href="https://arxiv.org/abs/1602.07839">Tight bounds on discrete quantitative Helly numbers</a>, arXiv:1602.07839 [math.CO], 2016. See Fig. 3 p. 5. %H A298562 G. Averkov, B. González Merino, I. Paschke, M. Schymura, and S. Weltge, <a href="https://doi.org/10.1016/j.aam.2017.04.003">Tight bounds on discrete quantitative Helly numbers</a>, Adv. in Appl. Math., 89 (2017), 76--101. %H A298562 Wouter Castryck, <a href="https://doi.org/10.1007/s00454-011-9376-2">Moving Out the Edges of a Lattice Polygon</a>, Discrete Comput. Geom., 47 (2012), p. 496-518. %H A298562 Wouter Castryck, <a href="https://homes.esat.kuleuven.be/~wcastryc/# :~:text=Moving%20out%20the%20edges%20of%20a%20lattice%20polygon">Homepage</a>. See the accompanying files for the above-referenced paper. %H A298562 Günter Rote, <a href="/A298562/a298562.txt">Table of n, a(n) for n = 0..200</a> together with a corresponding a(n)-gon for each n, (2023). %e A298562 a(18) = 11 (so this sequence differs from A322345), attained only by the following polygon (No. 3736 in the corresponding list in Castryck's file) with 11 vertices, 1 non-vertex boundary lattice point, and genus (number of internal lattice points) 17: [(-2, -1), (-1, -2), (1, -2), (3, -1), (4, 0), (4, 1), (3, 2), (1, 3), (0, 3), (-1, 2), (-2, 0)]. %o A298562 (Python) # See the Python program for A322345. %Y A298562 Cf. A298755, A322345. %K A298562 nonn %O A298562 0,1 %A A298562 _Bernardo González Merino_, Jan 21 2018 %E A298562 a(31) onwards from _Günter Rote_, Oct 01 2023