|
| |
|
|
A084616
|
|
Maximum number of circles of diameter 1 that can be packed in a square of area n (i.e. with side length n^(1/2)).
|
|
4
| |
|
|
1, 1, 2, 4, 4, 5, 5, 6, 9, 9, 9, 10, 12, 13, 14, 16, 16, 16, 18, 19, 20, 21, 22, 23, 25, 25, 26, 27, 28, 30, 30, 31, 33, 33, 34, 36, 36, 39, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 52, 52, 53, 53, 55, 56, 57, 58, 59, 59, 61, 62, 63, 65, 68, 68, 68, 69, 69, 70, 72, 73, 74, 74
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| Most sequence terms beyond n=20 are only conjectures supported by comprehensive numerical results. No proof is available for the following observations: n=30 is the first case were a square of area < n (29.74921576) is sufficient to cover n circles. The first case were more than n circles can be covered occurs for n=38. The required area to cover 39 circles is 37.76050335. n=59 is the last case where a square of area n does not suffice to cover n+1 circles (60 circles require square area 59.11626524).
|
|
|
REFERENCES
| P.G. Szabo et al, New Approaches to Circle Packing in a Square. Vol. 6 in Optimization and Its Applications, Springer 2007.
|
|
|
LINKS
| Hugo Pfoertner, Minimum area of square needed to cover n circles of diameter 1.
E. Specht, The best known packings of equal circles in the unit square.
|
|
|
EXAMPLE
| a(2)=1 because a square of side length sqrt(2)=1.414.. is not large enough to cover two circles of diameter 1 (the required side length would be 1+sqrt(2)/2=1.707..
a(38)=39 because 39 circles fit into a square of area 38.
|
|
|
CROSSREFS
| Cf. A051657, A084617, A084618.
Sequence in context: A036437 A053306 A108422 * A196259 A071193 A071192
Adjacent sequences: A084613 A084614 A084615 * A084617 A084618 A084619
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Jun 01 2003
|
| |
|
|
