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A298562 Quantitative (polygonal) Helly numbers for the integer lattice Z^2. 2
4, 6, 6, 6, 8, 7, 8, 9, 8, 8, 10, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 11, 11, 12, 12, 12, 13, 12, 12, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) = g(Z^2,n) is the maximum integer k>0 such that there exists a lattice polygon containing n+k lattice points with exactly k vertices.

LINKS

Table of n, a(n) for n=0..30.

G. Averkov, B. González Merino, I. Paschke, M. Schymura, S. Weltge, Tight bounds on discrete quantitative Helly numbers, arXiv:1602.07839 [math.CO], 2016. See Fig. 3 p. 5.

G. Averkov, B. González Merino, I. Paschke, M. Schymura, S. Weltge, Tight bounds on discrete quantitative Helly numbers, Adv. in Appl. Math., 89 (2017), 76--101.

W. Castryck, Moving Out the Edges of a Lattice Polygon, Discrete Comput. Geom., 47 (2012), p. 496-518.

CROSSREFS

Cf. A298755.

Sequence in context: A029854 A329502 A141328 * A298755 A035551 A087573

Adjacent sequences:  A298559 A298560 A298561 * A298563 A298564 A298565

KEYWORD

nonn,more

AUTHOR

Bernardo González Merino, Jan 21 2018

STATUS

approved

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Last modified February 26 18:29 EST 2020. Contains 332293 sequences. (Running on oeis4.)