A344676 The number of n X n binary orthogonal matrices having an equal number of ones in each row.

1, 2, 6, 48, 120, 1440, 5040, 2903040, 203575680, 41157849600, 2414207980800

Offset: 1

Author

Nathan J. Russell, May 26 2021

Keywords

• nonn
• hard
• more

Comments

The inverse of an orthogonal matrix is its transpose. This implies the dot product of a row with itself must be 1. This further implies the number of ones in each row must be odd. Given that orthogonal matrices form a group, it must be the case the transpose is also an orthogonal matrix. This requires every column of a binary orthogonal matrix also have an odd number of ones.

For 1 <= n <= 4 the counts are the same for the total number of binary orthogonal matrices (A003053).

Examples

			a(7) = 5040. There are 5040 7 X 7 binary orthogonal matrices where all rows have an equal number of ones.
		

Crossrefs

Cf. A003053.

Extensions

a(9)-a(10) from Martin Ehrenstein, Jun 13 2021

a(11) from Martin Ehrenstein, Jun 16 2021