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A111368
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The number of maximal determinant {-1,1} matrices of order n.
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0
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 5, 3, 3, 3, 3, 7
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,11
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COMMENTS
| The number of inequivalent maximal determinant {-1,1} matrices of order n where two matrices are considered equivalent if one can be obtained from the other by permuting rows, permuting columns and multiplying rows or columns by -1. Additional terms: a(24)=60, a(25)=78, a(28)=487. The terms a(4n) are given in sequence A007299.
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REFERENCES
| J. H. E. Cohn, On the number of D-optimal designs, J. Combin. Theory Ser. A 66 (1994) 214-225.
Warren D. Smith, Studies in Computational Geometry Motivated by Mesh Generation, Ph. D. dissertation, Princeton University (1988).
J. Williamson, Determinants whose elements are 0 and 1, Amer. Math. Monthly 53 (1946) 427-434.
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LINKS
| R. P. Brent, W. P. Orrick, J. Osborn, and P. Zimmermann, Maximal determinants and saturated D-optimal designs of orders 19 and 37.
W. P. Orrick, On the enumeration of some D-optimal designs, preprint, 2005.
W. P. Orrick and B. Solomon, The Hadamard maximal determinant problem
E. Spence, Ted Spence's home page, website.
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CROSSREFS
| Cf. A003433, A007299.
Sequence in context: A046534 A131324 A079724 * A140750 A028264 A010122
Adjacent sequences: A111365 A111366 A111367 * A111369 A111370 A111371
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KEYWORD
| hard,nonn
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AUTHOR
| William P. Orrick (worrick(AT)indiana.edu), Nov 08 2005
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EXTENSIONS
| Added a(19)-a(21) and Brent et al. reference.
Edited by Will Orrick, 20 December 2011.
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