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A003433
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Hadamard maximal determinant problem: largest determinant of (+1,-1)-matrix of order n.
(Formerly M1291)
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12
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1, 2, 4, 16, 48, 160, 576, 4096, 14336, 73728, 327680, 2985984, 14929920, 77635584, 418037760, 4294967296, 21474836480, 146028888064, 894426939392, 10240000000000, 59392000000000, 409600000000000
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OFFSET
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1,2
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COMMENTS
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I added the entry for n=22 since this has been proved optimal by Chasiotis et al (reference in A003432). [Richard P. Brent, Aug 17 2021]
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REFERENCES
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Ed Hughes and Rob Pratt, New Features in SAS/OR 13.1, SAS Paper SAS256-2014.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
See A003432 for further references, links and formulas.
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LINKS
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FORMULA
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a(n) <= n^(n/2).
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MATHEMATICA
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A003432 = Cases[Import["https://oeis.org/A003432/b003432.txt", "Table"], {_, _}][[All, 2]];
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CROSSREFS
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A003432 is the main entry for this sequence.
Cf. A188895 (number of distinct matrices having this maximal determinant).
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KEYWORD
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nonn,hard,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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