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 A343746 #9 Apr 28 2021 20:39:17 %S A343746 0,0,0,0,1,2,0,-1,1,0,0,-1,0,1,1,0,-1,0,0,1,-1,0,0,1,0,-1,-1,2,-1,-2, %T A343746 1,-1,0,-1,0,0,-1,1,2,1,2,2,2,2,0,1,0,0,-1,-1,0,-1,-2,2,1,-2,3,2,0,3, %U A343746 2,-2,2,3,0,2,3,-2,1,2,-2,3,2,-3,1,0,-4,1,-2,-3,1,-2,-2,3,-3,0,3,-2,2 %N A343746 The x,y,z coordinates of the points visited by a knight on a 3D cubic lattice using the step rules given in A343678. %C A343746 See A343678 for the rules determining the knight's steps on the cubic lattice and for images of the resulting path. %e A343746 a(1),a(2),a(3) = 0,0,0. The knight starts at the origin on the lattice. %e A343746 a(4),a(5),a(6) = 0,1,2. The 24 points the knight could step to on the first step all have only 1 visited neighbor and are all the same distance from the origin. Also they all have coordinates as arrangements of 0,+-1,+-2 thus the only way they can be separated is using rules 5 and 6 of A343678 which selects the smallest magnitudes of the x,y,z coordinates followed by the largest absolute x,y,z coordinates. This leads to the point (0,1,2) being selected. %e A343746 a(7),a(8),a(9) = 0,-1,1. The other two possible points which have the same number of visited neighbors and are the same distance from the origin are (1,1,0) and (-1,1,0), but (0,-1,1) is chosen as that has the minimum x-coordinate magnitude. %e A343746 a(52),a(53),a(54) = -1,-2,2. This is the first point that is chosen due to having the maximum product of the absolute values of its coordinate. %e A343746 a(577),a(578),a(579) = -2,-3,-1. This is the first point that is stepped to that has two visited neighboring points. %e A343746 a(1978),a(1979),a(1980) = -3,3,7. This is the first point that is stepped to that has three visited neighboring points. %Y A343746 Cf. A343678 (point square distances from origin), A343747 (point x coordinates), A343748 (point y coordinates), A343749 (point z coordinates) A330189, A329520, A316667. %K A343746 sign,fini %O A343746 1,6 %A A343746 _Scott R. Shannon_, Apr 27 2021