%I #28 Jun 16 2021 04:08:24

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

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

%C 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.

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

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

%Y Cf. A003053.

%K nonn,hard,more

%O 1,2

%A _Nathan J. Russell_, May 26 2021

%E a(9)-a(10) from _Martin Ehrenstein_, Jun 13 2021

%E a(11) from _Martin Ehrenstein_, Jun 16 2021