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 1-5 of 5 results.

A289158 Number of unlabeled connected loopless multigraphs with n nodes of degree 4 or less and with at most double edges.

Original entry on oeis.org

1, 1, 2, 7, 28, 112, 590, 3419, 23453, 178599, 1516692, 14083855, 142029043, 1542152723, 17925912574, 221938298129, 2914638247016, 40455853460661, 591654481313077, 9091698010380468, 146433114305147508, 2466517505722469501, 43361349681960337334
Offset: 0

Views

Author

Natan Arie Consigli, Jul 04 2017

Keywords

Comments

In chemical terms this counts the following molecules (excluding stereoisomers) without triple bonds, given n carbon atoms:
- carbon allotropes;
- aliphatic hydrocarbons;
- resonance structures of graphically non-equivalent anti-aromatic and aromatic hydrocarbons;
Some molecules are theoretical and may or may not exist.

Links

Crossrefs

Cf. A121941, A289157 (allows more than two edges), A303030, A303031.

Programs

  • nauty
    geng -c -D4 ${n} -q | multig -m2 -D4 -u

Extensions

a(15)-a(22) from Andrew Howroyd, Mar 20 2020

A303032 Number of unlabeled connected graphs with n nodes of degree 5 or less.

Original entry on oeis.org

1, 1, 1, 2, 6, 21, 112, 697, 6386, 75700, 1156842, 21503340, 471142472, 11851753163, 336605142326, 10661879669294, 373171677147769, 14326039970010402, 599529134063451455, 27206654007549974712, 1332697569146848014994, 70181910345392508318643, 3959059626001669328959513
Offset: 0

Views

Author

Natan Arie Consigli, Jun 04 2018

Keywords

Crossrefs

Cf. A303031 (also counts double edged graphs), A303033 (at most triple edges).
Cf. A121941 (degree 4 or less), A243393 (degree 3 or less).

Programs

  • nauty
    for n in {1..12}; do geng -c -D5 ${n} -u; done

Extensions

a(13)-a(22) from Andrew Howroyd, Mar 20 2020

A303033 Number of unlabeled connected loopless multigraphs with n nodes of degree 5 or less and with single, double or triple edges.

Original entry on oeis.org

1, 1, 3, 12, 81, 535, 5274, 60684, 869238, 14595645, 284939257, 6347472749, 159579271688, 4482770916274, 139578090353236, 4783834092385411, 179397242557917048, 7322223973235272082, 323760818899998259561, 15443359560966718348986, 791699492870169123493379
Offset: 0

Views

Author

Natan Arie Consigli, Jun 04 2018

Keywords

Crossrefs

Cf. A134818, A303030, A303031, A303032.

Programs

  • nauty
    for n in {1..11}; do geng -c -D5 ${n}  -q | multig  -m3 -D5 -u;

Extensions

a(12)-a(20) from Andrew Howroyd, Mar 20 2020

A303030 Number of unlabeled connected loopless multigraphs with n nodes of degree 3 or less and with single or double edges.

Original entry on oeis.org

1, 1, 2, 4, 12, 22, 68, 166, 534, 1589, 5464, 18579, 68320, 255424, 1000852, 4018156, 16671976, 70890940, 309439942, 1381815168, 6310880471, 29428287639, 140012980007, 678970863717, 3353545264060, 16857749613964, 86191265140699, 447951112379963, 2365177154077186
Offset: 0

Views

Author

Natan Arie Consigli, Apr 17 2018

Keywords

Comments

For n >= 1, a(n) is also the number of hydronitrogen molecules containing only n nitrogen trivalent (octet rule satisfying) atoms. So for example, diazene is counted but hydrazoic acid is not because the former has only trivalent nitrogens and the latter has two non-trivalent nitrogens.
Some of the molecules are theoretical and may or may not exist due to their strained geometries.
Apparently the same as A243391 for n > 2. - Georg Fischer, Oct 16 2018
This is the case since A243391 gives the number of loopless multigraphs with nodes of degree 3 or less. The extra graph in A243391 is the 3-regular graph on 2 nodes. - Andrew Howroyd, Mar 20 2020

Examples

			a(3) = 4 because there are 4 molecules satisfying the above condition: triazane, triazene, triazirine, triazidirine.
Note: hydrazoic acid is not counted because there are 2 nitrogens not satisfying the octet rule (one has a positive formal charge and the other one has a negative one).
Graphically, a(3) = 4 because there are 4 graphs satisfying the above condition: the linear graph, the linear graph with one double edge, the triangle graph, and the triangle graph with one double edge. - _Michael B. Porter_, Apr 28 2018

Crossrefs

Cf. A134818, A243391, A289158, A303031.

Programs

  • nauty
    for n in {1..18}; do geng -c -D3 ${n}  -q | multig -m2 -D3 -u;done

Formula

a(n) = A243391(n) for n > 2. - Andrew Howroyd, Mar 20 2020

Extensions

a(20)-a(28) from Andrew Howroyd, Mar 20 2020

A334547 Number of unlabeled connected loopless multigraphs with n nodes of degree 5 or less.

Original entry on oeis.org

1, 1, 5, 14, 93, 602, 5847, 66289, 937696, 15575285, 301360805, 6663874305, 166516898890, 4654082023569, 144301649717895, 4928171085359360, 184252862642720722, 7501009857590958129, 330928677041195111955, 15754816518916261088582, 806306082299053607173143
Offset: 0

Views

Author

Andrew Howroyd, May 05 2020

Keywords

Crossrefs

Column k=5 of A334546.
Cf. A303031, A303032, A303033, A333896.

Formula

Inverse Euler transform of A333896.
Showing 1-5 of 5 results.

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