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A325476
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Number of connected regular loopless multigraphs on n unlabeled nodes of degree less than n.
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1
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1, 1, 1, 1, 3, 7, 75, 984, 105831, 35494648, 53493557150, 250087643676776, 4520743153498327817, 272584534800111470995411
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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Multigraphs are loopless.
Initial terms computed using nauty and traces.
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LINKS
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Table of n, a(n) for n=0..13.
Brendan McKay and Adolfo Piperno, Nauty and Traces
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FORMULA
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a(n) = Sum_{k=0..n-1} A328682(n, k). - Andrew Howroyd, Mar 18 2020
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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Cf. A289988, A289986, A319896, A319897, A324218, A325474, A328682.
Sequence in context: A191485 A119572 A172995 * A234536 A103737 A354480
Adjacent sequences: A325473 A325474 A325475 * A325477 A325478 A325479
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KEYWORD
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nonn,more,hard
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AUTHOR
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Natan Arie Consigli, May 02 2019
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EXTENSIONS
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a(10)-a(13) from Andrew Howroyd, Mar 18 2020
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STATUS
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approved
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