A051661 Experimental values for number of circles in packing equal circles into a square for which there are no loose circles.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 23, 24, 25, 27, 30, 34, 35, 36, 37, 38, 39, 42, 52, 56, 67, 68, 77, 80, 86, 87, 99, 120, 137, 143, 150, 188

Offset

0,2

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..39.

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 TAMSASS-PECS Algorithm, Optimization Theory: Recent Developments from Mátraháza, Kluwer Academic Publishers, Dordrecht, 2001, pp. 207-224.

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. 287-293.

K. J. Nurmela and Patric R. J. Östergård, Packing up to 50 equal circles in a square, Discrete Comput. Geom. 18 (1997) 1, p. 111-120.

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. 191-206.

Crossrefs

Complement of A051660.

Sequence in context: A364560 A097752 A014866 * A051037 A250089 A257997

Adjacent sequences: A051658 A051659 A051660 * A051662 A051663 A051664

Keyword

nonn

Author

Eckard Specht (eckard.specht(AT)physik.uni-magdeburg.de)

Extensions

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

Status

approved