

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
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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

Wouter Castryck, Homepage. See the accompanying files for the abovereferenced paper.


EXAMPLE

a(18) = 11 (so this sequence differs from A322345), attained only by the following polygon (No. 3736 in the corresponding list in Castryck's file) with 11 vertices, 1 nonvertex boundary lattice point, and genus (number of internal lattice points) 17: [(2, 1), (1, 2), (1, 2), (3, 1), (4, 0), (4, 1), (3, 2), (1, 3), (0, 3), (1, 2), (2, 0)].


CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



