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A007299 Number of Hadamard matrices of order 4n.
(Formerly M3736)
1, 1, 1, 1, 5, 3, 60, 487, 13710027 (list; graph; refs; listen; history; text; internal format)



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.

The Hadamard conjecture is that a(n) > 0 for all n >= 0. - Charles R Greathouse IV, Oct 08 2012


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

F. J. Aragon Artacho, J. M. Borwein, M. K. Tam, Douglas-Rachford Feasibility Methods for Matrix Completion Problems, 2013; http://www.carma.newcastle.edu.au/~jb616/DR_MatrixCompletion.pdf

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

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

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

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

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

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

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

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

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

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


Table of n, a(n) for n=0..8.

Hadi Kharaghani, Home Page

Hadi Kharaghani and B. Tayfeh-Rezaie, Hadamard matrices of order 32, J. Combin. Designs 21 (2013) no. 5, 212-221 [DOI]

W. P. Orrick, Switching operations for Hadamard matrices, arxiv:math.CO/0507515. (Gives lower bounds for a(8) and a(9))

N. J. A. Sloane, Tables of Hadamard matrices

N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).

Eric Weisstein's World of Mathematics, Hadamard Matrix

Index entries for sequences related to Hadamard matrices


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

Sequence in context: A323779 A027858 A181755 * A257935 A109254 A258091

Adjacent sequences:  A007296 A007297 A007298 * A007300 A007301 A007302




N. J. A. Sloane


a(8) from the H. Kharaghani and B. Tayfeh-Rezaie paper. - N. J. A. Sloane, Feb 11 2012



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Last modified October 14 04:44 EDT 2019. Contains 327995 sequences. (Running on oeis4.)