A306608 Table read by antidiagonals: T(x,y) is the minimum size of a planar additive basis for the rectangle [0,x]*[0,y], for x,y >= 0.

1, 2, 2, 2, 3, 2, 3, 4, 4, 3, 3, 5, 4, 5, 3, 4, 5, 6, 6, 5, 4, 4, 6, 6, 7, 6, 6, 4, 4, 6, 7, 8, 8, 7, 6, 4, 4, 7, 8, 9, 8, 9, 8, 7, 4, 5, 7, 8, 9, 10, 10, 9, 8, 7, 5, 5, 8, 8, 10, 10, 11, 10, 10, 8, 8, 5, 5, 8, 10, 11, 11, 12, 12, 11, 11, 10, 8, 5

Offset

0,2

Comments

A planar additive basis is a set of points with nonnegative integer coordinates such that their pairwise sums cover a given rectangle of points with integer coordinates. Pairwise sums of a point with itself are included.

T(x,y) = T(y,x).

Links

Table of n, a(n) for n=0..77.

J. Kohonen, V. Koivunen and R. Rajamäki, Planar additive bases for rectangles, Journal of Integer Sequences, 21 (2018), Article 18.9.8. [see Table 2]

Example

The table starts:
  1, 2, 2, 3, 3, 4, 4, ...
  2, 3, 4, 5, 5, 6, ...
  2, 4, 4, 6, 6, ...
  3, 5, 6, 7, ...
  3, 5, 6, ...
  4, 6, ...
  4, ...
  ...
T(6,3)=9: The rectangle [0,6]*[0,3] has the following minimum basis of 9 elements, with elements marked as "*", and empty locations as "-".
  3  *------
  2  ---*---
  1  **-*---
  0  ***--*-
     0123456

Crossrefs

Main diagonal is A295771.

Sequence in context: A360998 A165015 A178994 * A143976 A194296 A194336

Adjacent sequences: A306605 A306606 A306607 * A306609 A306610 A306611

Keyword

nonn,tabl

Author

Jukka Kohonen, Feb 28 2019

Status

approved