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%I #18 Apr 11 2019 07:25:51
%S 1,3,4,7,8,11,12,14,16,19,20,23,24,26
%N a(n) is the minimum size of a planar additive basis for the square [0,n]^2.
%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 a(n) <= 2n+1, because there is an L-shaped basis of that size.
%C a(n) <= 2n if n is even and nonzero, because of a square-shaped "boundary basis" with sides at coordinates 0 and n/2.
%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.
%e a(3)=7: The square [0,3]^2 is covered by the pairwise sums of the L-shaped basis {(0,0),(1,0),(2,0),(3,0),(0,1),(0,2),(0,3)}, which has 7 elements.
%Y A295774 is the restricted version.
%Y A001212 concerns the one-dimensional problem.
%Y Main diagonal of A306608.
%K nonn,more
%O 0,2
%A _Jukka Kohonen_, Nov 27 2017
%E a(12), a(13) from _Jukka Kohonen_, Dec 17 2018
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