

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



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
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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. 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

Main diagonal is A295771.
Sequence in context: A167505 A165015 A178994 * A143976 A194296 A194336
Adjacent sequences: A306605 A306606 A306607 * A306609 A306610 A306611


KEYWORD

nonn,tabl


AUTHOR

Jukka Kohonen, Feb 28 2019


STATUS

approved



