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A007299 Number of Hadamard matrices of order 4n.
(Formerly M3736)

%I M3736

%S 1,1,1,1,5,3,60,487,13710027

%N Number of Hadamard matrices of order 4n.

%C More precisely, number of inequivalent Hadamard matrices of order n if two matrices are considered equivalent if one can be obtained from the other by permuting rows, permuting columns and multiplying rows or columns by -1.

%C The Hadamard conjecture is that a(n) > 0 for all n >= 0. - _Charles R Greathouse IV_, Oct 08 2012

%D V. Alvarez, J. A. Armario, M. D. Frau and F. Gudlel, The maximal determinant of cocyclic (-1, 1)-matrices over D_{2t}, Linear Algebra and its Applications, 2011, in press; doi:10.1016/j.laa.2011.05.018

%D J. Hadamard, R├ęsolution d'une question relative aux d├ęterminants, Bull. des Sciences Math. 2 (1893), 240-246.

%D H. Kharaghani and B. Tayfeh-Rezaie, On the classification of Hadamard matrices of order 32, J. Combin. Des., 18 (2010), 328-336.

%D H. Kharaghani and B. Tayfeh-Rezaie, Hadamard matrices of order 32, math.ipm.ac.ir/tayfeh-r/papersandpreprints/H32typetwo.pdf

%D Kimura, H., (1986), Hadamard matrices of order 28 with automorphism groups of order two, J. Combin. Theory, A 43, 98-102.

%D Kimura, H., (1989), New Hadamard matrix of order 24, Graphs Combin., 5, 235-242.

%D Kimura, H., (1994), Classification of Hadamard matrices of order 28 with Hall sets, Discrete Math., 128, 257-268.

%D Kimura, H., (1994), Classification of Hadamard matrices of order 28, Discrete Math., 133, 171-180.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D Spence, Edward; Classification of Hadamard matrices of order 24 and 28. Discrete Math. 140 (1995), no. 1-3, 185-243.

%D Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 1073, 2002.

%H F. J. Aragon Artacho, J. M. Borwein, M. K. Tam, <a href="https://carma.newcastle.edu.au/resources/jon/DR_MatrixCompletion.pdf">Douglas-Rachford Feasibility Methods for Matrix Completion Problems</a>, March 2014.

%H Hadi Kharaghani, <a href="http://www.cs.uleth.ca/~hadi/">Home Page</a>

%H Hadi Kharaghani and B. Tayfeh-Rezaie, <a href="http://math.ipm.ac.ir/tayfeh-r/Hadamard32.htm">Hadamard matrices of order 32</a>, J. Combin. Designs 21 (2013) no. 5, 212-221. [<a href="http://dx.doi.org/10.1002/jcd.21323">DOI</a>]

%H W. P. Orrick, <a href="https://arxiv.org/abs/math/0507515">Switching operations for Hadamard matrices</a>, arXiv:math/0507515 [math.CO], 2005-2007. (Gives lower bounds for a(8) and a(9))

%H N. J. A. Sloane, <a href="http://neilsloane.com/hadamard/">Tables of Hadamard matrices</a>

%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/sg.txt">My favorite integer sequences</a>, in Sequences and their Applications (Proceedings of SETA '98).

%H Warren D. Smith, <a href="/A007299/a007299.c.txt">C program for generating Hadamard matrices of various orders</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HadamardMatrix.html">Hadamard Matrix</a>

%H <a href="/index/Ha#Hadamard">Index entries for sequences related to Hadamard matrices</a>

%Y Cf. A096201, A036297, A048615, A048616, A003432, A048885.

%K hard,nonn,nice

%O 0,5

%A _N. J. A. Sloane_

%E a(8) from the H. Kharaghani and B. Tayfeh-Rezaie paper. - _N. J. A. Sloane_, Feb 11 2012

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Last modified July 31 04:12 EDT 2021. Contains 346367 sequences. (Running on oeis4.)