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

J. Kohonen, V. Koivunen and R. RajamÃ¤ki, 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

KEYWORD

nonn,tabl

AUTHOR

Jukka Kohonen, Feb 28 2019

STATUS

approved