cp's OEIS Frontend

A325476 Number of connected regular loopless multigraphs on n unlabeled nodes of degree less than n.

%I A325476 #39 Jun 02 2025 17:23:52
%S A325476 1,1,1,1,3,7,75,984,105831,35494648,53493557150,250087643676776,
%T A325476 4520743153498327817,272584534800111470995411
%N A325476 Number of connected regular loopless multigraphs on n unlabeled nodes of degree less than n.
%C A325476 Multigraphs are loopless.
%C A325476 Initial terms computed using nauty and traces.
%H A325476 Brendan McKay and Adolfo Piperno, <a href="http://pallini.di.uniroma1.it">Nauty and Traces</a>
%F A325476 a(n) = Sum_{k=0..n-1} A328682(n, k). - _Andrew Howroyd_, Mar 18 2020
%e A325476 There is no such thing as a graph with nodes of negative degree, and the "nodeless" graph has, according to the definition in the name, zero nodes of degree less than 0. So a(0) = 1.
%o A325476 (nauty)
%o A325476 for ((n=2; n<9; n++)); do
%o A325476 a=0
%o A325476 for ((d=0; d<${n}; d++)); do
%o A325476 s=$(geng -c -d1 ${n} -q | multig -r${d} -u 2>&1 | cut -d ' ' -f 7 | grep -v '^$')
%o A325476 a=$((a+s))
%o A325476 done
%o A325476 echo ${a}
%o A325476 done
%o A325476 # _Andrey Zabolotskiy_, Sep 26 2019
%Y A325476 Cf. A289988, A289986, A319896, A319897, A324218, A325474, A328682.
%K A325476 nonn,more,hard
%O A325476 0,5
%A A325476 _Natan Arie Consigli_, May 02 2019
%E A325476 a(10)-a(13) from _Andrew Howroyd_, Mar 18 2020