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A003433 Hadamard maximal determinant problem: largest determinant of (+1,-1)-matrix of order n.
(Formerly M1291)
10
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; text; internal format)
OFFSET

1,2

REFERENCES

Ed Hughes and Rob Pratt, New Features in SAS/OR 13.1, SAS Paper SAS256-2014; file:///Users/njasloane/Downloads/SAS256_Hughes_FinalPaper.pdf

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 formulae.

LINKS

Table of n, a(n) for n=1..21.

Richard P. Brent and Judy-anne H. Osborn, On minors of maximal determinant matrices, arXiv preprint arXiv:1208.3819, 2012.

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

Index entries for sequences related to maximal determinants

FORMULA

a(n) = 2^(n-1)*A003432(n-1). E.g., a(6) = 32*A003432(5) = 32*5 = 160.

a(n) <= n^(n/2).

CROSSREFS

A003432 is the main entry for this sequence.

Cf. A051753.

Cf. A188895 (number of distinct matrices having this maximal determinant).

Sequence in context: A119000 A034917 A215724 * A153951 A248748 A165905

Adjacent sequences:  A003430 A003431 A003432 * A003434 A003435 A003436

KEYWORD

nonn,hard,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

Added a(19)-a(21).

Edited by William P. Orrick, Dec 20 2011

STATUS

approved

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Last modified November 25 18:09 EST 2014. Contains 250000 sequences.