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

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

Table of n, a(n) for n=0..13.

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

Crossrefs

Cf. A289988, A289986, A319896, A319897, A324218, A325474, A328682.

Sequence in context: A119572 A362651 A172995 * A234536 A103737 A354480

Adjacent sequences: A325473 A325474 A325475 * A325477 A325478 A325479

Keyword

nonn,more,hard

Author

Natan Arie Consigli, May 02 2019

Extensions

a(10)-a(13) from Andrew Howroyd, Mar 18 2020

Status

approved