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.

A058929 Number of 2-connected claw-free labeled cubic graphs with 2n nodes.

Original entry on oeis.org

0, 1, 60, 2520, 453600, 59875200, 10897286400, 6701831136000, 2623194782208000, 1338096104497152000, 1633313557551836160000, 1324107982344764897280000, 1408369399403068118016000000
Offset: 1

Views

Author

N. J. A. Sloane, Jan 12 2001

Keywords

References

  • G.-B. Chae, E. M. Palmer and R. W. Robinson, Computing the number of Claw-free Cubic Graphs with given Connectivity, preprint, 2001.

Crossrefs

Cf. A057848 (1-connected).

A084659 Number of labeled claw-free cubic graphs on 2n nodes (not necessarily connected).

Original entry on oeis.org

1, 0, 1, 60, 2555, 466200, 62791575, 14536021500, 8381453705625, 3284480337138000, 1942832950684250625, 2143745512307546647500, 1743194710893176557891875, 2022583790860881671548125000
Offset: 0

Views

Author

Gordon F. Royle, Jun 02 2003

Keywords

Crossrefs

Cf. A057848.

Programs

  • Maple
    cfc[0] := 1; cfc[1] := 0; cfc[n+1] := (6*n-5)*binomial(2*n+1,3)*cfc[n-1] + 60*(2*n^2-7)*binomial(2*n+1,5)*cfc[n-2] + 420*(12*n-31)*binomial(2*n+1,7)*cfc[n-3] - 60480*(4*n-19)*binomial(2*n+1,9)*cfc[n-4] - 3326400*(6*n^2-54*n+127)*binomial(2*n+1,11)*cfc[n-5] - 172972800*(9*n^2-108*n+347)*binomial(2*n+1,13)*cfc[n-6] - 54486432000*(n-1)*binomial(2*n+1,15)*cfc[n-7] + 59281238016000*(n-7)*binomial(2*n+1,17)*cfc[n-8] + 422378820864000*(18*n-97)*binomial(2*n+1,19)*cfc[n-9] + 6563766876226560000*binomial(2*n+1,21)*cfc[n-10] + 673229602575129600000*binomial(2*n+1,23)*cfc[n-11];

Formula

Recurrence is given in Maple code below. For asymptotics see the 2003 paper.

A084656 Number of unlabeled connected claw-free cubic graphs on 2n vertices.

Original entry on oeis.org

0, 1, 1, 1, 1, 3, 3, 5, 11, 15, 27, 54, 94, 181, 369, 731, 1502, 3187
Offset: 1

Views

Author

Gordon F. Royle, Jun 02 2003

Keywords

Comments

A cubic graph is claw-free (contains no induced K_{1,3}) if and only if every vertex lies in a triangle. All graphs counted are simple (no loops or multiple edges).

Examples

			K_4 is claw-free and so a(2) = 1, while the triangular prism is the only claw-free cubic graph on 6 vertices, so a(3) = 1.
		

References

  • A. Itzhakov and M. Codish, Breaking Symmetries with High Dimensional Graph Invariants and their Combination, Proceedings of the 20th International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research (2023).

Crossrefs

Extensions

a(16)-a(18) from Michael Codish, Mar 05 2023
Showing 1-3 of 3 results.