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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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8
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
See A003432 for references, links and formulae.
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LINKS
| W. P. Orrick and B. Solomon, Large-determinant sign matrices of order 4k+1, Discr. Math. 307 (2007), 226-236.
Eric Weisstein's World of Mathematics, -11-Matrix
Index entries for sequences related to binary matrices
Index entries for sequences related to Hadamard matrices
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FORMULA
| a(n) = 2^(n-1)*A003432(n-1). E.g. a(6) = 32*A003432(5) = 32*5 = 160.
a(n) <= n^(n/2).
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CROSSREFS
| A003432 is the main entry for this sequence.
Cf. A051753.
Cf. A188895 (number of distinct matrices having this maximal determinant).
Sequence in context: A103435 A119000 A034917 * A153951 A165905 A104354
Adjacent sequences: A003430 A003431 A003432 * A003434 A003435 A003436
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KEYWORD
| nonn,hard,nice,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Added a(19)-a(21).
Edited by Will Orrick, 20 December 2011
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