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

1,4

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.

Links

Table of n, a(n) for n=1..12.

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

Formula

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

Example

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

Crossrefs

Cf. A189889, A084616, A084617.

Sequence in context: A257058 A189889 A329451 * A034809 A336900 A096808

Adjacent sequences: A308575 A308576 A308577 * A308579 A308580 A308581

Keyword

nonn,hard,more

Author

Ethan D. Kidd, Jun 08 2019

Status

approved