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.

A172286 Numbers of circuits of length 2n in K_{n,n} (the complete bipartite graph on 2n vertices).

This page as a plain text file.
%I A172286 #22 May 07 2024 07:05:41
%S A172286 2,32,1458,131072,19531250,4353564672,1356446145698,562949953421312,
%T A172286 300189270593998242,200000000000000000000,162805498773679522226642,
%U A172286 158993694406781688266883072,183466660386537233316799232018
%N A172286 Numbers of circuits of length 2n in K_{n,n} (the complete bipartite graph on 2n vertices).
%C A172286 Circuits are allowed to be self-intersecting and are directional with a designated start node. The number of (self-avoiding) directed cycles is given by A010790. - _Andrew Howroyd_, Sep 05 2018
%H A172286 Andrew Howroyd, <a href="/A172286/b172286.txt">Table of n, a(n) for n = 1..100</a>
%F A172286 a(n) = 2*n^(2*n).
%e A172286 a(2) = 32 because there are 32 circuits of length 4 in the complete bipartite graph K2,2.
%o A172286 (MATLAB)
%o A172286 nmax = 10;
%o A172286 for k=1:nmax
%o A172286 an = 2*k^(2*k);
%o A172286 fprintf('%3.0f ', an);
%o A172286 end
%o A172286 (PARI) a(n)=2*n^(2*n); \\ _Andrew Howroyd_, Sep 05 2018
%Y A172286 Cf. A010790, A118537.
%K A172286 easy,nonn
%O A172286 1,1
%A A172286 Thibaut Lienart (syncthib(AT)gmail.com), Jan 30 2010
%E A172286 More terms from _Max Alekseyev_, Jan 18 2012