A367497 Number of 4-regular loopless multigraphs on n vertices.

1, 0, 1, 1, 15, 158, 3355, 93708, 3535448, 170816680, 10307577384, 759439940230, 67095584693434, 7001532238614324, 851997581131397870, 119582892039683711842, 19176016845387328919910, 3484133398830462852182192, 712017802878894004029129622, 162597177988359237252433594350

Offset: 0

Author

Arick Grootveld, Nov 20 2023

Keywords

• nonn

Comments

Also this is the number of unique polynomials that can be created from products of differences between n terms, such that the polynomial expansion includes each term to the 4th power.

Examples

			For n=2, the only polynomial is: (x_1 - x_2)^4.
Which corresponds to the following adjacency matrix:
 [0,4
  4,0].
For n=3, the only polynomial is: (x_1 - x_2)^2 * (x_1 - x_3)^2 * (x_2 - x_3)^2.
Which corresponds to the following adjacency matrix:
 [0, 2, 2
  2, 0, 2
  2, 2, 0].
For n=4, an example of a polynomial would be (x_1 - x_3)^3 * (x_1 - x_4)^1 * (x_2 - x_3)^1 * (x_2 - x_4)^3 = (x_1^4 * x_2^4) + (x_3^4 * x_4^4) + ... + {other polynomial terms}.
And this corresponds to the following adjacency matrix:
 [0, 0, 3, 1
  0, 0, 1, 3
  3, 1, 0, 0
  1, 3, 0, 0].
		

Crossrefs

Column k=4 of A333351.

Cf. A000217.