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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

%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. Rajamäki, <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

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Last modified August 19 08:08 EDT 2019. Contains 326115 sequences. (Running on oeis4.)