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
Examples
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.
Links
- Brendan McKay and Adolfo Piperno, Nauty and Traces
Programs
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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
Formula
a(n) = Sum_{k=0..n-1} A328682(n, k). - Andrew Howroyd, Mar 18 2020
Extensions
a(10)-a(13) from Andrew Howroyd, Mar 18 2020
Comments