This site is supported by donations to The OEIS Foundation.



Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A003433 Hadamard maximal determinant problem: largest determinant of (+1,-1)-matrix of order n.
(Formerly M1291)
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)



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.


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


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

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


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




N. J. A. Sloane


Added a(19)-a(21).

Edited by William P. Orrick, Dec 20 2011



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 19 21:57 EST 2014. Contains 252240 sequences.