

A295771


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


2



1, 3, 4, 7, 8, 11, 12, 14, 16, 19, 20, 23, 24, 26
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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.
a(n) <= 2n+1, because there is an Lshaped basis of that size.
a(n) <= 2n if n is even and nonzero, because of a squareshaped "boundary basis" with sides at coordinates 0 and n/2.


LINKS

Table of n, a(n) for n=0..13.
J. Kohonen, V. Koivunen and R. RajamÃ¤ki, 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 Lshaped basis {(0,0),(1,0),(2,0),(3,0),(0,1),(0,2),(0,3)}, which has 7 elements.


CROSSREFS

A295774 is the restricted version.
A001212 concerns the onedimensional problem.
Main diagonal of A306608.
Sequence in context: A070874 A187582 A288553 * A285503 A327221 A014601
Adjacent sequences: A295768 A295769 A295770 * A295772 A295773 A295774


KEYWORD

nonn,more


AUTHOR

Jukka Kohonen, Nov 27 2017


EXTENSIONS

a(12), a(13) from Jukka Kohonen, Dec 17 2018


STATUS

approved



