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Number of non-isomorphic n X n symmetric binary matrices with an equal number of ones in every row and column up to permutation of rows and columns.
4

%I #6 Mar 11 2020 18:05:32

%S 1,2,3,4,6,8,17,36,146,1066,15419,406684,19284912,1635874946,

%T 249424764407,68725494158824,34418706513939926,31487353344361957012,

%U 52887877379630894268187,163777247316556715401451972,939121048579630147375554814224

%N Number of non-isomorphic n X n symmetric binary matrices with an equal number of ones in every row and column up to permutation of rows and columns.

%C a(n) is the number of regular bicolored graphs on 2n unlabeled nodes which are invariant when the two color classes are interchanged.

%e The a(2) = 3 matrices are:

%e [0 0] [1 0] [1 1]

%e [0 0] [0 1] [1 1]

%Y Row sums of A333159.

%Y Cf. A122082, A322698, A333162.

%K nonn

%O 0,2

%A _Andrew Howroyd_, Mar 10 2020