A206711 Total number of distinct Hadamard matrices of order 4n.

768, 4954521600, 20251509535014912000, 88526812916367202104587059200000, 3776127947893930552689423154306445475840000000, 92624181047745713568610317051197596401168530978226831360000000, 886156947284057553944669848348035536068124589065755283423684984832000000000000

Offset: 1

Author

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

Keywords

• nonn
• nice

Comments

This is the total number of distinct Hadamard matrices of order 4n, ignoring all equivalences.

Links

• Brendan McKay, Table of n, a(n) for n = 1..8
• J. Dong, V. Elser, G. Gyawali, K. Y. Jee, J. Kent-Dobias, A. Mandaiya, M. Renz, Y. Su, Glass phenomenology in the hard matrix model, arXiv:1912.07558 [cond-mat.stat-mech], 2019.
• H. Kharaghani and B. Tayfeh-Rezaie, Hadamard matrices of order 32.
• Index entries for sequences related to Hadamard matrices

Crossrefs

Cf. A007299, A036297, A206712.

Formula

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

a(n) = A206712(4n).