A322345 Maximal number of vertices of a convex lattice polygon containing n lattice points in its interior.

4, 6, 6, 6, 8, 7, 8, 9, 8, 8, 10, 9, 9, 10, 10, 10, 10, 11, 10, 12, 12, 12, 11, 11, 12, 12, 12, 13, 12, 12, 13, 13, 13, 13, 14, 14, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 14, 15, 15, 15, 15, 15, 16, 15, 16, 15, 16, 16, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 16, 17, 17, 16, 17, 17

Offset

0,1

Comments

This is an inverse of A063984 in the following sense: A063984(k) = min {n : a(n)>=k}. Thus a(n) grows roughly like const*n^(1/3). - Günter Rote, Sep 19 2023

Links

Günter Rote, Table of n, a(n) for n = 0..200

Wouter Castryck, Moving Out the Edges of a Lattice Polygon, Discrete Comput. Geom., 47 (2012), p. 496-518, Column n_max in Table 1, p 512.

Wouter Castryck, Homepage. See the accompanying files for the above-referenced paper.

Günter Rote, Python program for this sequence and for A298562, (2023).

Günter Rote, Table of n, a(n) for n = 0..200 together with a corresponding a(n)-gon for each n, (2023).

Prog

(Python) # See the Python program in the links section.

Crossrefs

Cf. A063984, A187015, A322343, A322346, A298562, A298755.

Sequence in context: A029854 A329502 A141328 * A298562 A298755 A035551

Adjacent sequences: A322342 A322343 A322344 * A322346 A322347 A322348

Keyword

nonn

Author

Hugo Pfoertner, Dec 04 2018

Extensions

a(0) added by Andrey Zabolotskiy, Dec 29 2021

Name clarified by Günter Rote, Sep 18 2023

a(31) onwards from Günter Rote, Oct 01 2023

Status

approved