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A325476
Number of connected regular loopless multigraphs on n unlabeled nodes of degree less than n.
1
1, 1, 1, 1, 3, 7, 75, 984, 105831, 35494648, 53493557150, 250087643676776, 4520743153498327817, 272584534800111470995411
OFFSET
0,5
COMMENTS
Multigraphs are loopless.
Initial terms computed using nauty and traces.
LINKS
Brendan McKay and Adolfo Piperno, Nauty and Traces
FORMULA
a(n) = Sum_{k=0..n-1} A328682(n, k). - Andrew Howroyd, Mar 18 2020
EXAMPLE
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.
PROG
(bash+nauty)
for ((n=2; n<9; n++)); do
a=0
for ((d=0; d<${n}; d++)); do
s=$(geng -c -d1 ${n} -q | multig -r${d} -u 2>&1 | cut -d ' ' -f 7 | grep -v '^$')
a=$((a+s))
done
echo ${a}
done
# Andrey Zabolotskiy, Sep 26 2019
KEYWORD
nonn,more,hard
AUTHOR
Natan Arie Consigli, May 02 2019
EXTENSIONS
a(10)-a(13) from Andrew Howroyd, Mar 18 2020
STATUS
approved