cp's OEIS Frontend

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

%I A023393 #33 Jul 06 2023 06:38:53
%S A023393 0,1,2,7,11,19,27,38,50,64,80,98,118
%N A023393 Maximal number of circles of radius 1 that can be packed in a circle of radius n.
%C A023393 The terms for n>5 are only conjectures supported by extensive computations.
%D A023393 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 A023393 For list of references given by E. Specht, see the Specht link.
%H A023393 Claudio Chaib, <a href="https://community.wolfram.com/groups/-/m/t/1903990">GeometricScene: Circles in Circle packing (A023393 OEIS)</a>, Apr 02 2020.
%H A023393 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 A023393 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 A023393 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 A023393 Cf. A084618, A084617, A084644.
%Y A023393 Cf. A201993 (conjectured lower bounds for a(n)).
%K A023393 more,nonn,hard
%O A023393 0,3
%A A023393 _David W. Wilson_
%E A023393 Terms for n>5 from _Hugo Pfoertner_, Jun 01 2003
%E A023393 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 A023393 Edited by _N. J. A. Sloane_ at the suggestion of _David W. Wilson_, Sep 22 2007
%E A023393 Offset corrected by _Jon E. Schoenfield_, Oct 12 2008