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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. 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. LINKS Richard P. Brent and Judy-anne H. Osborn, On minors of maximal determinant matrices, arXiv preprint arXiv:1208.3819 [math.CO], 2012. Massimiliano Fasi, Gian Maria Negri Porzio, Determinants of Normalized Bohemian Upper Hessemberg Matrices, University of Manchester (England, 2019). 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 FORMULA a(n) = 2^(n-1)*A003432(n-1). E.g., a(6) = 32*A003432(5) = 32*5 = 160. a(n) <= n^(n/2). MATHEMATICA A003432 = Cases[Import["https://oeis.org/A003432/b003432.txt", "Table"], {_, _}][[All, 2]]; a[n_] := 2^(n-1) A003432[[n]]; a /@ Range[21] (* Jean-François Alcover, Jan 17 2020 *) 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 EXTENSIONS a(19)-a(21) added by William P. Orrick, Dec 20 2011 STATUS approved

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Last modified September 28 13:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)