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A333166
Number of n-regular graphs on 2n unlabeled vertices with half-edges.
3
1, 2, 3, 12, 118, 9638, 10622074, 135037240786, 18621890255342234, 28688490385422625653266, 511030957184968000138445253202
OFFSET
0,2
COMMENTS
A half-edge is like a loop except it only adds 1 to the degree of its vertex.
a(n) is the number of non-isomorphic 2n X 2n symmetric matrices with entries in {+1, -1} and all rows and columns summing to zero where isomorphism is up to simultaneous permutation of rows and columns. The case where rows and columns can be permuted independently is covered by A333165.
FORMULA
a(n) = A333161(2*n, n).
EXAMPLE
The a(1) = 1 matrix is:
[+ -]
[- +]
.
The a(2) = 2 matrices are:
[+ + - -] [- - + +] [+ + - -]
[+ + - -] [- - + +] [+ - + -]
[- - + +] [+ + - -] [- + - +]
[- - + +] [+ + - -] [- - + +]
CROSSREFS
Central coefficients of A333161.
Sequence in context: A088223 A162053 A162075 * A245584 A102878 A132501
KEYWORD
nonn,more
AUTHOR
Andrew Howroyd, Mar 12 2020
STATUS
approved