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

Author

Giedrius Alkauskas, Nov 04 2022

Keywords

• nonn
• hard
• more

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

• 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.

Extensions

a(5) from Giedrius Alkauskas, Oct 09 2023

a(6) from Giedrius Alkauskas, Nov 30 2023