A295774 - OEIS

%I #17 Dec 20 2018 09:20:10

%S 1,4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92

%N a(n) is the minimum size of a restricted planar additive basis for the square [0,2n]^2.

%C A planar additive basis for the square [0,2n]^2 is a set of points with nonnegative integer coordinates such that their pairwise sums cover the square. Self-sums are allowed. In a restricted basis all points are in the lower left quadrant [0,n]^2.

%C Matches A008574 at least up to a(23)=92.

%H J. Kohonen, V. Koivunen and R. Rajamäki, <a href="https://arxiv.org/abs/1711.08812">Planar additive bases for rectangles</a>, arXiv preprint arXiv:1711.08812, [math.NT], 2017.

%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(2)=8: the square [0,4]^2 is covered by the pairwise sums of {(0,0),(1,0),(2,0),(0,1),(2,1),(0,2),(1,2),(2,2)}, which has 8 elements.

%Y A295771 is the nonrestricted version.

%K nonn,more

%O 0,2

%A _Jukka Kohonen_, Nov 27 2017