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.
a(n) <= 2n+1, because there is an L-shaped basis of that size.
a(n) <= 2n if n is even and nonzero, because of a square-shaped "boundary basis" with sides at coordinates 0 and n/2.
LINKS
J. Kohonen, V. Koivunen and R. Rajamäki, Planar additive bases for rectangles, Journal of Integer Sequences, 21 (2018), Article 18.9.8.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jukka Kohonen, Nov 27 2017
EXTENSIONS
a(12), a(13) from Jukka Kohonen, Dec 17 2018
STATUS
approved