A333166 Number of n-regular graphs on 2n unlabeled vertices with half-edges.

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.

Links

Table of n, a(n) for n=0..10.

Formula

a(n) = A333161(2*n, n).

Cf. A333164, A333165.

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

Adjacent sequences: A333163 A333164 A333165 * A333167 A333168 A333169

Keyword

nonn,more

Author

Andrew Howroyd, Mar 12 2020

Status

approved