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 A333159 Triangle read by rows: T(n,k) is the number of non-isomorphic n X n symmetric binary matrices with k ones in every row and column up to permutation of rows and columns. 12
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 4, 5, 4, 1, 1, 1, 1, 4, 12, 12, 4, 1, 1, 1, 1, 7, 31, 66, 31, 7, 1, 1, 1, 1, 8, 90, 433, 433, 90, 8, 1, 1, 1, 1, 12, 285, 3442, 7937, 3442, 285, 12, 1, 1, 1, 1, 14, 938, 30404, 171984, 171984, 30404, 938, 14, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS Rows and columns may be permuted independently. The case that rows and columns must be permuted together is covered by A333161. T(n,k) is the number of k-regular bicolored graphs on 2n unlabeled nodes which are invariant when the two color classes are exchanged. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..230 FORMULA T(n,k) = T(n,n-k). EXAMPLE Triangle begins:   1;   1, 1;   1, 1,  1;   1, 1,  1,   1;   1, 1,  2,   1,    1;   1, 1,  2,   2,    1,    1;   1, 1,  4,   5,    4,    1,    1;   1, 1,  4,  12,   12,    4,    1,   1;   1, 1,  7,  31,   66,   31,    7,   1,  1;   1, 1,  8,  90,  433,  433,   90,   8,  1, 1;   1, 1, 12, 285, 3442, 7937, 3442, 285, 12, 1, 1;   ... The T(2,1) = 1 matrix is:   [1 0]   [0 1] . The T(4,2)= 2 matrices are:   [1 1 0 0]   [1 1 0 0]   [1 1 0 0]   [1 0 1 0]   [0 0 1 1]   [0 1 0 1]   [0 0 1 1]   [0 0 1 1] CROSSREFS Columns k=0..4 are A000012, A000012, A002865, A000840, A000843. Row sums are A333160. Central coefficients are A333165. Cf. A008327, A122082, A333157, A133687, A333161. Sequence in context: A047996 A227690 A063686 * A008327 A133687 A215870 Adjacent sequences:  A333156 A333157 A333158 * A333160 A333161 A333162 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, Mar 10 2020 STATUS approved

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Last modified April 13 15:23 EDT 2021. Contains 342936 sequences. (Running on oeis4.)