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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
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
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.
Sequence in context: A377060 A227690 A063686 * A008327 A133687 A215870
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Mar 10 2020
STATUS
approved