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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.

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.


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 [math.CO], 2012.

Ion Nechita, Some analytical aspects of Hadamard matrices.

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


a(19)-a(21) added by William P. Orrick, Dec 20 2011



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Last modified January 16 23:44 EST 2019. Contains 319206 sequences. (Running on oeis4.)