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A003433 Hadamard maximal determinant problem: largest determinant of (+1,-1)-matrix of order n.

%I A003433 M1291 #75 Feb 16 2025 08:32:27
%S A003433 1,2,4,16,48,160,576,4096,14336,73728,327680,2985984,14929920,
%T A003433 77635584,418037760,4294967296,21474836480,146028888064,894426939392,
%U A003433 10240000000000,59392000000000,409600000000000
%N A003433 Hadamard maximal determinant problem: largest determinant of (+1,-1)-matrix of order n.
%C A003433 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]
%D A003433 Ed Hughes and Rob Pratt, New Features in SAS/OR 13.1, SAS Paper SAS256-2014.
%D A003433 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A003433 See A003432 for further references, links and formulas.
%H A003433 Richard P. Brent and Judy-anne H. Osborn, <a href="http://arxiv.org/abs/1208.3819">On minors of maximal determinant matrices</a>, arXiv preprint arXiv:1208.3819 [math.CO], 2012.
%H A003433 Thomas Decru, Tako Boris Fouotsa, Paul Frixons, Valerie Gilchrist, and Christophe Petit, <a href="https://ia.cr/2024/1332">Attacking trapdoors from matrix products</a>, Cryptology ePrint Archive (2024) Paper 2024/1332.
%H A003433 Massimiliano Fasi and Gian Maria Negri Porzio, <a href="http://eprints.maths.manchester.ac.uk/2709/">Determinants of Normalized Bohemian Upper Hessemberg Matrices</a>, University of Manchester (England, 2019).
%H A003433 John Holbrook, Nathaniel Johnston, and Jean-Pierre Schoch, <a href="https://arxiv.org/abs/2206.02863">Real Schur norms and Hadamard matrices</a>, arXiv:2206.02863 [math.CO], 2022.
%H A003433 Ion Nechita, <a href="http://ion.nechita.net/wp-content/uploads/2016/09/had.pdf">Some analytical aspects of Hadamard matrices</a>.
%H A003433 William P. Orrick and B. Solomon, <a href="http://dx.doi.org/10.1016/j.disc.2006.04.041">Large-determinant sign matrices of order 4k+1</a>, Discr. Math. 307 (2007), 226-236.
%H A003433 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/-11-Matrix.html">-11-Matrix</a>
%H A003433 <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>
%H A003433 <a href="/index/Ha#Hadamard">Index entries for sequences related to Hadamard matrices</a>
%H A003433 <a href="/index/De#determinants">Index entries for sequences related to maximal determinants</a>
%F A003433 a(n) = 2^(n-1)*A003432(n-1). E.g., a(6) = 32*A003432(5) = 32*5 = 160.
%F A003433 a(n) <= n^(n/2).
%t A003433 A003432 = Cases[Import["https://oeis.org/A003432/b003432.txt", "Table"], {_, _}][[All, 2]];
%t A003433 a[n_] := 2^(n-1) A003432[[n]];
%t A003433 a /@ Range[21] (* _Jean-François Alcover_, Jan 17 2020 *)
%Y A003433 A003432 is the main entry for this sequence.
%Y A003433 Cf. A051753.
%Y A003433 Cf. A188895 (number of distinct matrices having this maximal determinant).
%K A003433 nonn,hard,nice
%O A003433 1,2
%A A003433 _N. J. A. Sloane_
%E A003433 a(19)-a(21) added by _William P. Orrick_, Dec 20 2011
%E A003433 a(22) added by _Richard P. Brent_, Aug 16 2021