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

Author

Hugo Pfoertner, Dec 04 2018

Keywords

• nonn

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).

Crossrefs

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

Programs

Python

# See the Python program in the links section.

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