A308578 Maximum number of non-overlapping circles of radius 1/n that can be placed inside a unit square.

0, 1, 1, 4, 5, 9, 10, 16, 20, 25, 30, 36

Offset: 1

Author

Ethan D. Kidd, Jun 08 2019

Keywords

• nonn
• hard
• more

Comments

Alternatively described as the maximum number of circles of unit radius that can be placed inside a square of side length n.

It appears that the terms a(2) to a(8) are equal to the related terms of A189889.

Examples

			a(6)=9 because 9 circles of radius 1/6 can be placed in a 3 X 3 regular grid inside a unit square.
		

Links

• E. Specht, The Best Known Packings of Equal Circles in a Square

Crossrefs

Cf. A189889, A084616, A084617.

Formula

a(2k) = A084617(k). - Jon E. Schoenfield, Jun 09 2019