cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A367497 #35 Nov 30 2023 19:18:10
%S A367497 1,0,1,1,15,158,3355,93708,3535448,170816680,10307577384,759439940230,
%T A367497 67095584693434,7001532238614324,851997581131397870,
%U A367497 119582892039683711842,19176016845387328919910,3484133398830462852182192,712017802878894004029129622,162597177988359237252433594350
%N A367497 Number of 4-regular loopless multigraphs on n vertices.
%C A367497 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.
%e A367497 For n=2, the only polynomial is: (x_1 - x_2)^4.
%e A367497 Which corresponds to the following adjacency matrix:
%e A367497  [0,4
%e A367497   4,0].
%e A367497 For n=3, the only polynomial is: (x_1 - x_2)^2 * (x_1 - x_3)^2 * (x_2 - x_3)^2.
%e A367497 Which corresponds to the following adjacency matrix:
%e A367497  [0, 2, 2
%e A367497   2, 0, 2
%e A367497   2, 2, 0].
%e A367497 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}.
%e A367497 And this corresponds to the following adjacency matrix:
%e A367497  [0, 0, 3, 1
%e A367497   0, 0, 1, 3
%e A367497   3, 1, 0, 0
%e A367497   1, 3, 0, 0].
%Y A367497 Column k=4 of A333351.
%Y A367497 Cf. A000217.
%K A367497 nonn
%O A367497 0,5
%A A367497 _Arick Grootveld_, Nov 20 2023