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 A160826 #5 Jun 02 2025 01:41:50 %S A160826 0,0,0,0,0,0,0,0,1,2,5,4,3,0,0,0,1,0,0,0,0,2,4,5,1,3,1,0,3,2,3,4,3,4, %T A160826 5,6,9,4,3,0,1,0,0,0,2,4,3,4,5,10,14,3,6,0,7,0,4,5,1,8,6,0,4,7,8,6,5, %U A160826 11,5,9,12,12,4,0,11,7,12,0,3,1,0,1,5,0,6,2,10,11,25,17,3,2,0,9,0,12,5,0,4,2 %N A160826 Improvement of A125852 over A053416, A053479 and A053417. %C A160826 How many more lattice points of a hexagonal lattice can be covered by placing a disk of diameter n at an optimal center instead of one of the three obvious centers (a lattice point, midpoint between two lattice points, barycenter of a fundamental triangle)? %C A160826 The first difference occurs at n=9, when a diameter 9 disc around e.g. (1/2, 4*sqrt(5)) covers more lattice points than one around (0,0) or (1/2,0) or (1/2,sqrt(3)/6). %C A160826 Clearly a(n) = O(n) as all "extra" points have norm approximately n^2/4 if the optimal center is chosen near (0,0). Does a(n)/n converge? Are there only finitely many n with a(n)=0? %H A160826 H. v. Eitzen, <a href="/A160826/b160826.txt">Table of n, a(n) for n=1..1000</a> %F A160826 a(n) = A125852(n) - max(A053416(n),A053479(n),A053417(n)) %e A160826 For diameters n=2,4,6,8 a disc around (0,0) and for n=1,3,5,7 a disc around(1/2,0) happens to be optimal (covers as many points as possible); therefore a(1)=a(2)=...=a(8)=0. %e A160826 a(9) = A125852(9) - max(A053416(9),A053479(9),A053417(9)) = 77 - max(73,69,76) = 1. %K A160826 nonn %O A160826 1,10 %A A160826 _Hagen von Eitzen_, May 27 2009