A341730 Maximum number of sides in any cell in a regular 2n-gon with all diagonals drawn (cf. A007678).

3, 4, 4, 5, 4, 5, 6, 7, 8, 8, 6, 8, 8, 6, 7, 8, 8, 8, 12, 8, 10, 8, 10, 10, 8, 10, 10, 10, 9, 10, 10, 9, 10, 10, 10, 10, 12, 10, 10, 10, 10, 10, 10, 10, 14, 10, 10, 10, 10, 12, 12, 10, 11, 10, 12, 10, 12, 12, 14, 14, 12, 12, 12, 12, 14, 12, 12

Offset: 2

Author

Scott R. Shannon and N. J. A. Sloane, Mar 06 2021

Keywords

• nonn

Comments

A bisection of A341729.

a(46) = 14, corresponding to a regular 92-gon, suggesting that this sequence may be unbounded (cf. A342222). (The Pfetsch-Ziegler web page discusses a similar question for polygons defined by grid points.) It would be nice to have a b-file.

For which values of n is a(n) odd (and why)?

Links

• M. E. Pfetsch and G. M. Ziegler, Large chambers in a lattice polygon, December 13, 2004;
• M. E. Pfetsch and G. M. Ziegler, Large chambers in a lattice polygon [Local copy of webpage, pdf only]

Crossrefs

Cf. A007678, A062361, A331450, A331451, A341729, A342222.