A358212 a(n) is the maximal possible sum of squares of the side lengths of an n^2-gon supported on a subset 1 <= x,y <= n of an integer lattice.

4, 10, 36, 98, 232

Offset

2,1

Comments

Examples show that a(7) >= 462, a(8) >= 842, a(9) >= 1424, a(10) >= 2242.

Asymptotics: liminf a(n)/n^4 >= 8/27, limsup a(n)/n^4 <= 2/3.

Links

Table of n, a(n) for n=2..6.

Oliver Mantas Ališauskas, Grid connector, Web application for this problem.

Oliver Mantas Ališauskas, Giedrius Alkauskas, and Valdas Dičiūnas, Full Grid Lattice Polygons with Maximal Sum of Squares of Edge-Lengths, arXiv:2311.03011 [math.CO], 2023-2024.

S. Chow, A. Gafni, and P. Gafni, Connecting the dots: maximal polygons on a square grid, Math. Mag. 94 (2021), no. 2, 118-124.

G. L. Cohen and E. Tonkes, Dartboard arrangements, Elect. J. Combin., 8(2) (2001), #R4.

Crossrefs

Cf. A209077, A110611, A064842, A226595, A226596.

Sequence in context: A220205 A196880 A359688 * A088013 A149179 A149180

Adjacent sequences: A358209 A358210 A358211 * A358213 A358214 A358215

Keyword

nonn,hard,more

Author

Giedrius Alkauskas, Nov 04 2022

Extensions

a(5) from Giedrius Alkauskas, Oct 09 2023

a(6) from Giedrius Alkauskas, Nov 30 2023

Status

approved