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]
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Mar 10 2020
STATUS
approved