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 1-3 of 3 results.

A289987 Number of unlabeled connected loopless multigraphs with n nodes of degree less than n.

Original entry on oeis.org

0, 1, 1, 2, 12, 146, 5847, 716141, 300635753, 430472002801, 2117649544384420, 36154420408979339192, 2165755991529764630384554, 459803603042851200545393118005
Offset: 0

Views

Author

Natan Arie Consigli, Aug 19 2017

Keywords

Comments

Multigraphs are loopless.

Examples

			From _Gheorghe Coserea_, Oct 11 2017: (Start)
For n=4 the a(4)=12 solutions are:
o--o--o--o   o==o--o--o   o--o==o--o   o==o--o==o
o--o         o==o         o==o
|  |         |  |         |  |
o--o         o--o         o==o
o--o         o==o
| /          | /
|/           |/
o--o         o--o
o---o        o--o         o--o--o
|\ /|        | /|            |
| x |        |/ |            o
|/ \|        o--o
o---o
(End)

Crossrefs

A diagonal of A334546.
Cf. A001349, A289988.

Programs

  • nauty
    for n in {1..8}; do geng -c -D$[${n}-1] ${n} -q | multig -m$[${n}-1] -D$[${n}-1] -u; done

Extensions

a(9)-a(13) from Andrew Howroyd, May 05 2020

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.

Links

Crossrefs

Cf. A289988, A289986, A319897.

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.

Links

Crossrefs

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

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 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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