A023393 - OEIS

%I #33 Jul 06 2023 06:38:53

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

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

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

%D 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.

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

%H Claudio Chaib, <a href="https://community.wolfram.com/groups/-/m/t/1903990">GeometricScene: Circles in Circle packing (A023393 OEIS)</a>, Apr 02 2020.

%H R. L. Graham, B. D. Lubachevsky, K. J. Nurmela, and P. R. J. Östergård, <a href="https://doi.org/10.1016/S0012-365X(97)00050-2">Dense Packings of Congruent Circles in a Circle</a>, Discrete Mathematics 181 (1998), 139-154.

%H B. D. Lubachevsky and  R. L. Graham, <a href="https://doi.org/10.1007/PL00009314">Curved Hexagonal Packings of Equal Disks in a Circle</a>, Discrete Comput. Geom. 18 (1997), 179-194.

%H E. Specht, <a href="http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html">The best known packings of equal circles in the unit circle</a>

%Y Cf. A084618, A084617, A084644.

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

%K more,nonn,hard

%O 0,3

%A _David W. Wilson_

%E Terms for n>5 from _Hugo Pfoertner_, Jun 01 2003

%E 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, ...

%E Edited by _N. J. A. Sloane_ at the suggestion of _David W. Wilson_, Sep 22 2007

%E Offset corrected by _Jon E. Schoenfield_, Oct 12 2008