A393934 - OEIS

A393934

Array T(n,k) read by antidiagonals, n,k >= 1: Start with a point at the origin of the n-dimensional grid. At each iteration, add a new point by increasing one of the coordinates of the current point by 1, choosing the option that gives the least maximum number of points on a line through the new point. In case of ties, compare the number of points on the line with the next largest number of points, etc. If there is still a tie, choose the first among the optimal coordinates. T(n,k) is the zero-based index of the coordinate that is increased in the k-th step.

%I #5 Mar 11 2026 10:19:58

%S 0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,2,0,1,0,0,0,0,2,0,1,0,0,0,1,0,2,0,

%T 1,0,0,1,0,1,0,2,0,1,0,0,0,0,0,1,0,2,0,1,0,0,1,1,3,0,1,0,2,0,1,0,0,1,

%U 0,0,3,0,1,0,2,0,1,0,0,1,2,1,0,3,0,1,0,2,0,1,0

%N Array T(n,k) read by antidiagonals, n,k >= 1: Start with a point at the origin of the n-dimensional grid. At each iteration, add a new point by increasing one of the coordinates of the current point by 1, choosing the option that gives the least maximum number of points on a line through the new point. In case of ties, compare the number of points on the line with the next largest number of points, etc. If there is still a tie, choose the first among the optimal coordinates. T(n,k) is the zero-based index of the coordinate that is increased in the k-th step.

%F T(n,k) = A007814(k) for 1 <= k < 2^n.

%e Array begins:

%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

%e ---+-----------------------------------------------

%e 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

%e 2 | 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 1

%e 3 | 0 1 0 2 0 1 0 0 1 0 2 0 1 0 0 1

%e 4 | 0 1 0 2 0 1 0 3 0 1 0 2 0 1 0 0

%e 5 | 0 1 0 2 0 1 0 3 0 1 0 2 0 1 0 4

%Y Rows 1-3 are A000004, A393932, A393933.

%Y Cf. A007814.

%K nonn,tabl

%O 1,18

%A _Pontus von Brömssen_, Mar 04 2026