A101201 Maximal number of kings in the toroidal king's graph on an n X n board such that each king is attacking no more than four other kings.

0, 2, 5, 9, 15, 21, 28, 37, 47, 60, 71, 84

Offset: 1

Author

Eugen J. Ionascu, Aug 12 2008

Keywords

• nonn
• more

Comments

All the numbers listed so far were calculated using LpSolveIDE. It can be shown that the sequence of densities a(n)/n^2 has a limit as n goes to infinity, which is the supremum of all the elements in the sequence. With the help of the computer, it was shown that a(n) is not more than 0.608956n^2.

Examples

			a(2)=2 because one can check that any arrangement of two kings will satisfy the requirement but any arrangement of three kings will not.
		

Links

• E. J. Ionascu, D. Pritkin and S. E. Wright, k-Dependence and Domination in Kings Graphs, Amer. Math. Monthly, vol. 115, no. 9, (2008), pp. 820-836.

Crossrefs

Cf. A103139, A189889.

Formula

a(n) is approximately 3n^2/5 (conjecture).