OFFSET
1,1
COMMENTS
Sequence terms for n>5 are only conjectures. The arrangement of 37 circles consists of one central circle surrounded by 3 rings of 6,12 and 18 circles. For n=7, 49 of the 55 circles are arranged in a rigid hexagonal lattice with 6 "rattlers" inserted in gaps at the circumference.
REFERENCES
List of references given by E. Specht; see corresponding link.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..85
Jerry Donovan, Packing Circles in Squares and Circles Page.
Hugo Pfoertner, Minimum area of circle needed to cover n circles of area 1
E. Specht, The sequence of N's that establish density records - provides continuation of the sequence.
EXAMPLE
a(4)=7 because the density 0.7777.. of the best packing of 7 circles (1 central circle surrounded by 6 neighbors) exceeds the density 0.68629.. of the packing of 4 circles arranged in a square.
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Jun 01 2003
EXTENSIONS
More terms from Robert G. Wilson v, Nov 07 2012
STATUS
approved