A023393 Maximal number of circles of radius 1 that can be packed in a circle of radius n.

0, 1, 2, 7, 11, 19, 27, 38, 50, 64, 80, 98, 118

Offset

0,3

Comments

The terms for n>5 are only conjectures supported by extensive computations.

References

R. L. Graham and B. D. Lubachevsky, Dense packings of 3k(k+1)+1 equal disks in a circle for k = 1, 2, 3, 4 and 5, Proc. First Int. Conf. "Computing and Combinatorics" COCOON'95, Springer Lecture Notes in Computer Science 959 (1996), 303-312.

For list of references given by E. Specht, see the Specht link.

Links

Table of n, a(n) for n=0..12.

Claudio Chaib, GeometricScene: Circles in Circle packing (A023393 OEIS), Apr 02 2020.

R. L. Graham, B. D. Lubachevsky, K. J. Nurmela, and P. R. J. Östergård, Dense Packings of Congruent Circles in a Circle, Discrete Mathematics 181 (1998), 139-154.

B. D. Lubachevsky and  R. L. Graham, Curved Hexagonal Packings of Equal Disks in a Circle, Discrete Comput. Geom. 18 (1997), 179-194.

E. Specht, The best known packings of equal circles in the unit circle

Crossrefs

Cf. A084618, A084617, A084644.

Cf. A201993 (conjectured lower bounds for a(n)).

Sequence in context: A105881 A060191 A178899 * A084619 A236478 A106906

Adjacent sequences: A023390 A023391 A023392 * A023394 A023395 A023396

Keyword

more,nonn,hard

Author

David W. Wilson

Extensions

Terms for n>5 from Hugo Pfoertner, Jun 01 2003

Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Feb 18 2004, writes to suggest that the sequence probably continues 138, 161, 187, 213, 242, 272, 304, 337, 373, 413, 451, 495, ...

Edited by N. J. A. Sloane at the suggestion of David W. Wilson, Sep 22 2007

Offset corrected by Jon E. Schoenfield, Oct 12 2008

Status

approved