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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 (list; graph; refs; listen; history; text; internal format)
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: 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

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Last modified February 6 01:28 EST 2023. Contains 360091 sequences. (Running on oeis4.)