A001441 Number of inequivalent Costas arrays of order n under dihedral group.

1, 1, 1, 2, 6, 17, 30, 60, 100, 277, 555, 990, 1616, 2168, 2467, 2648, 2294, 1892, 1283, 810, 446, 259, 114, 25, 12, 8, 29, 89, 23

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more
• nice

Comments

Dihedral group of order 8 acts by rotations and reflections of the square.

References

• James K Beard, Jon C Russo, Keith Erickson, Michael Moneleone and Mike Wright, Combinatoric collaboration on Costas arrays and radar applications, Proceedings of the IEEE 2004 Radar Conference, April 26-29 2004, ISBN 0-7803-8234-X, pp. 260-265 (entries for orders 24 and 25).
• James K Beard, Jon C Russo, Keith Erickson, Michael Moneleone and Mike Wright,"Costas Array Generation and Search Methodology," to appear in IEEE Transactions on Aerospace and Electronic Engineering. (Order 26)
• CRC Handbook of Combinatorial Designs, C. Colbourn and J. Dinitz, Editors, 1996, IV.7: Costas Arrays by Herbert Taylor (IV.7.6, page 259, Table 2.29).
• CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 227 (contains errors).

Links

• K. Drakakis, Results of the enumeration of Costas arrays of order 27, Slides, 2008.

Crossrefs

Cf. A008404, A001440, A001442, A008403.

Extensions

a(24)-a(26) from James K Beard (jkbeard(AT)comcast.net), Dec 04 2005

a(27) (from the Drakakis link) sent by John Healy (johnjhealy(AT)gmail.com), Jul 17 2008

a(28) and a(29) (from http://www.costasarrays.org/), Joerg Arndt, Jun 08 2012.