

A051660


Experimental values for number of circles in packing equal circles into a square for which there is a loose circle.


1



7, 11, 13, 14, 17, 19, 21, 22, 26, 28, 29, 31, 32, 33, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 81, 82, 83, 84, 85, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100
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OFFSET

0,1


REFERENCES

H. T. Croft, K. J. Falconer and R. K. Guy: Unsolved problems in geometry, Springer, New York, 1991.


LINKS

Table of n, a(n) for n=0..64.
D. Boll, Optimal Packing Of Circles And Spheres
L. G. Casado, I. García, P. G. Szabó, and T. Csendes, Packing Equal Circles in a Square II.  New Results for up to 100 Circles Using the TAMSASSPECS Algorithm, Optimization Theory: Recent Developments from Mátraháza, Kluwer Academic Publishers, Dordrecht, 2001, pp. 207224.
E. Friedman, Erich's Packing Center
C. D. Maranas, C. A. Floudas and P. M. Pardalos, New results in the packing of equal circles in a square, Discrete Mathematics 142 (1995), p. 287293.
K. J. Nurmela and Patric R. J. Östergård, Packing up to 50 equal circles in a square, Discrete Comput. Geom. 18 (1997) 1, p. 111120.
E. Specht, www.packomania.com
P. G. Szabó, Packing up to 100 circles in a square.
P. G. Szabó, T. Csendes, L. G. Casado, and I. García, Packing Equal Circles in a Square I.  Problem Setting and Bounds for Optimal Solutions, Optimization Theory: Recent Developments from Mátraháza, Kluwer Academic Publishers, Dordrecht, 2001, pp. 191206.


CROSSREFS

Sequence in context: A110547 A279622 A247819 * A187040 A028784 A119393
Adjacent sequences: A051657 A051658 A051659 * A051661 A051662 A051663


KEYWORD

nonn


AUTHOR

Eckard Specht (eckard.specht(AT)physik.unimagdeburg.de)


EXTENSIONS

I do not know how many of these values have been rigorously proved.  N. J. A. Sloane


STATUS

approved



