

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
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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..n1} 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: A191485 A119572 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



