A206711 -id:A206711 - cp's OEIS frontend

A199006 Related to number of Hadamard matrices of order 4n.

192, 21504, 190080, 10838016, 16440, 823616, 74306

Offset: 1

N. J. A. Sloane, Nov 01 2011

It seems that Álvarez et al. calculate these numbers by summing the orders of Aut(H) over inequivalent Hadamard matrices H. If so, a(8) = 20643963716 from Kharaghani and Tayfeh-Rezaie's Table 3. - Andrei Zabolotskii, Jul 08 2025

V. Álvarez, J. A. Armario, M. D. Frau, and F. Gudiel, The maximal determinant of cocyclic (-1, 1)-matrices over D_{2t}, Linear Algebra and its Applications, 2011, Volume 436, Issue 4, 15 February 2012, Pages 858-873. See Table 2. The terms a(1)-a(7) are said to be computed from the data from N. J. A. Sloane's website.
Hadi Kharaghani and Behruz Tayfeh-Rezaie, Hadamard Matrices of Order 32, Journal of Combinatorial Designs, 21 (2013), 212-221; see also preprint.
N. J. A. Sloane, A Library of Hadamard Matrices.

Cf. A007299, A048615, A048616, A199005, A199007, A206711.

A206712 Total number of distinct Hadamard matrices of order n.

Original entry on oeis.org

2, 8, 0, 768, 0, 0, 0, 4954521600, 0, 0, 0, 20251509535014912000, 0, 0, 0, 88526812916367202104587059200000, 0, 0, 0, 3776127947893930552689423154306445475840000000, 0, 0, 0, 92624181047745713568610317051197596401168530978226831360000000, 0, 0, 0, 886156947284057553944669848348035536068124589065755283423684984832000000000000, 0, 0, 0

Offset: 1

Brendan McKay, Feb 11 2012 (entered by N. J. A. Sloane)

a(n) is the total number of distinct Hadamard matrices of order n, ignoring all equivalences.

Brendan McKay, Table of n, a(n) for n = 1..35
F. J. Aragon Artacho, J. M. Borwein, M. K. Tam, Douglas-Rachford Feasibility Methods for Matrix Completion Problems, March 2014.
H. Kharaghani and B. Tayfeh-Rezaie, Hadamard matrices of order 32
Index entries for sequences related to Hadamard matrices

Cf. A007299, A036297, A206711.

a(4n) = A206711(n) = A048615(n)/A048616(n) * (2^n * n!)^2.

For n>1, a(4n+1) = a(4n+2) = a(4n+3) = 0.

cp's OEIS Frontend

A199006 Related to number of Hadamard matrices of order 4n.

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