cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A344676 #28 Jun 16 2021 04:08:24
%S A344676 1,2,6,48,120,1440,5040,2903040,203575680,41157849600,2414207980800
%N A344676 The number of n X n binary orthogonal matrices having an equal number of ones in each row.
%C A344676 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 A344676 For 1 <= n <= 4 the counts are the same for the total number of binary orthogonal matrices (A003053).
%e A344676 a(7) = 5040. There are 5040 7 X 7 binary orthogonal matrices where all rows have an equal number of ones.
%Y A344676 Cf. A003053.
%K A344676 nonn,hard,more
%O A344676 1,2
%A A344676 _Nathan J. Russell_, May 26 2021
%E A344676 a(9)-a(10) from _Martin Ehrenstein_, Jun 13 2021
%E A344676 a(11) from _Martin Ehrenstein_, Jun 16 2021