

A084644


Best packings of m>1 equal circles into a larger circle setting a new density record.


4



2, 3, 4, 7, 19, 37, 55, 85, 121, 147, 148, 150, 151, 187, 188, 190, 191, 192, 193, 198, 199, 235, 241, 264, 267, 269, 270, 291, 292, 293, 294, 295, 343, 346, 347, 348, 349, 408, 409, 412, 414, 415, 417, 418, 419, 420, 421, 481, 499, 564, 565, 649, 689, 690, 721
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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 best known packings of equal circles in the unit circle
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

Cf. A051657 (density records for circles packed into square), A084618, A023393.
Sequence in context: A110705 A139439 A119330 * A208729 A270777 A100686
Adjacent sequences: A084641 A084642 A084643 * A084645 A084646 A084647


KEYWORD

nonn


AUTHOR

Hugo Pfoertner, Jun 01 2003


EXTENSIONS

More terms from Robert G. Wilson v, Nov 07 2012


STATUS

approved



