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.

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, 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, 0, 0, 3, 0, 1, 0, 2, 0, 1, 0, 0, 1, 2, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0

Offset

1,18

Links

Table of n, a(n) for n=1..91.

Formula

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

Example

Array begins:
  n\k| 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16
  ---+-----------------------------------------------
   1 | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
   2 | 0  1  0  0  1  0  0  1  0  1  1  1  1  0  1  1
   3 | 0  1  0  2  0  1  0  0  1  0  2  0  1  0  0  1
   4 | 0  1  0  2  0  1  0  3  0  1  0  2  0  1  0  0
   5 | 0  1  0  2  0  1  0  3  0  1  0  2  0  1  0  4

Crossrefs

Rows 1-3 are A000004, A393932, A393933.

Cf. A007814.

Sequence in context: A231642 A288318 A354099 * A219483 A239927 A069846

Adjacent sequences: A393931 A393932 A393933 * A393935 A393936 A393937

Keyword

nonn,tabl

Author

Pontus von Brömssen, Mar 04 2026

Status

approved