cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A319896 Number of connected non-regular multigraphs with n nodes of degree up to n.

Original entry on oeis.org

0, 1, 0, 3, 31, 595, 33931, 6020479, 3613415171
Offset: 0

Views

Author

Natan Arie Consigli, Sep 30 2018

Keywords

Comments

Multigraphs are loopless.
Terms computed using nauty traces.

Crossrefs

Formula

a(n) = A289988(n) - A319897(n).

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

Original entry on oeis.org

1, 1, 1, 1, 3, 7, 75, 984, 105831, 35494648, 53493557150, 250087643676776, 4520743153498327817, 272584534800111470995411
Offset: 0

Views

Author

Natan Arie Consigli, May 02 2019

Keywords

Comments

Multigraphs are loopless.
Initial terms computed using nauty and traces.

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.
		

Crossrefs

Programs

  • 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
Showing 1-2 of 2 results.