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. 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
KEYWORD
nonn,tabl
AUTHOR
Jukka Kohonen, Feb 28 2019
STATUS
approved