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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
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, 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, 5, 5, 8, 10, 11, 11, 12, 12, 11, 11, 10, 8, 5 (list; table; graph; refs; listen; history; text; internal format)
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.

T(x,y) = T(y,x).

LINKS

Table of n, a(n) for n=0..77.

J. Kohonen, V. Koivunen and R. Rajamäki, Planar additive bases for rectangles, Journal of Integer Sequences, 21 (2018), Article 18.9.8. [see Table 2]

EXAMPLE

The table starts:

  1, 2, 2, 3, 3, 4, 4, ...

  2, 3, 4, 5, 5, 6, ...

  2, 4, 4, 6, 6, ...

  3, 5, 6, 7, ...

  3, 5, 6, ...

  4, 6, ...

  4, ...

  ...

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 "-".

  3  *------

  2  ---*---

  1  **-*---

  0  ***--*-

     0123456

CROSSREFS

Main diagonal is A295771.

Sequence in context: A167505 A165015 A178994 * A143976 A194296 A194336

Adjacent sequences:  A306605 A306606 A306607 * A306609 A306610 A306611

KEYWORD

nonn,tabl

AUTHOR

Jukka Kohonen, Feb 28 2019

STATUS

approved

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Last modified July 17 14:39 EDT 2019. Contains 325106 sequences. (Running on oeis4.)