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A344676
The number of n X n binary orthogonal matrices having an equal number of ones in each row.
0
1, 2, 6, 48, 120, 1440, 5040, 2903040, 203575680, 41157849600, 2414207980800
OFFSET
1,2
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).
EXAMPLE
a(7) = 5040. There are 5040 7 X 7 binary orthogonal matrices where all rows have an equal number of ones.
CROSSREFS
Cf. A003053.
Sequence in context: A072444 A334807 A052596 * A098710 A337907 A052614
KEYWORD
nonn,hard,more
AUTHOR
Nathan J. Russell, May 26 2021
EXTENSIONS
a(9)-a(10) from Martin Ehrenstein, Jun 13 2021
a(11) from Martin Ehrenstein, Jun 16 2021
STATUS
approved