%I
%S 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,
%T 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,
%U 5,5,8,10,11,11,12,12,11,11,10,8,5
%N 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.
%C 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.
%C T(x,y) = T(y,x).
%H J. Kohonen, V. Koivunen and R. RajamÃ¤ki, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL21/Rajamaki/raj.html">Planar additive bases for rectangles</a>, Journal of Integer Sequences, 21 (2018), Article 18.9.8. [see Table 2]
%e The table starts:
%e 1, 2, 2, 3, 3, 4, 4, ...
%e 2, 3, 4, 5, 5, 6, ...
%e 2, 4, 4, 6, 6, ...
%e 3, 5, 6, 7, ...
%e 3, 5, 6, ...
%e 4, 6, ...
%e 4, ...
%e ...
%e 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 "".
%e 3 *
%e 2 *
%e 1 ***
%e 0 ****
%e 0123456
%Y Main diagonal is A295771.
%K nonn,tabl
%O 0,2
%A _Jukka Kohonen_, Feb 28 2019
