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.

A006443 Number of achiral planar maps with n edges.

Original entry on oeis.org

1, 2, 4, 14, 47, 184, 761, 3314, 14997, 69886, 333884, 1626998, 8067786, 40580084, 206734083, 1064666724, 5536480877, 29036188788, 153450351924, 816503772830, 4371551433888
Offset: 0

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Keywords

Comments

An achiral map is a map with a sense-reversing automorphism.
The planar maps considered are connected and may contain loops and parallel edges. - Andrew Howroyd, Jan 13 2025

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Column k=0 of A380234.
Cf. A006384 (sensed), A006385 (unsensed), A006444 (2-connected), A006445 (3-connected).

Formula

a(n) = 2*A006385(n) - A006384(n). [Liskovets eq 3a] - R. J. Mathar, Oct 01 2011

Extensions

a(0)=1 prepended by Andrew Howroyd, Jan 13 2025
a(20) added by Andrew Howroyd, Jan 20 2025

A006403 Number of unsensed 2-connected planar maps with n edges.

Original entry on oeis.org

0, 1, 2, 3, 6, 15, 36, 114, 396, 1565, 6756, 31563, 154370, 785113, 4099948, 21870704, 118624544, 652485364, 3631820462, 20426666644, 115949791342, 663640383400, 3826858500878, 22218232389849, 129802836253994
Offset: 1

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Author

Keywords

Comments

The maps considered here may include parallel edges. - Andrew Howroyd, Jan 13 2025

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
  • Timothy R. Walsh, personal communication.

Crossrefs

Row sums of A379432.
Cf. A000139 (rooted), A006385, A006402 (sensed), A006407 (without parallel edges), A006444 (achiral).

Formula

a(n) = (A006402(n) + A006444(n))/2. - Andrew Howroyd, Jan 13 2025

Extensions

a(23)-a(25) added by Andrew Howroyd, Jan 13 2025

A010357 Number of unlabeled nonseparable (or 2-connected) loopless multigraphs with n edges.

Original entry on oeis.org

1, 1, 2, 3, 6, 14, 32, 90, 279, 942, 3468, 13777, 57747, 254671, 1170565, 5580706, 27487418, 139477796, 727458338, 3893078684, 21346838204, 119787629215, 687200870250
Offset: 1

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Author

Keywords

Comments

Original name: Multi-edge stars with n edges.

Examples

			From _Andrew Howroyd_, Nov 23 2020: (Start)
The a(1) = 1 graph is a single edge (K_2 = P_2).
The a(2) = 1 graph is a double edge.
The a(3) = 2 graphs are a triple edge and the triangle (K_3).
The a(4) = 3 graphs are a quadruple edge, a triangle with one double edge and the square (C_4).
(End)
		

Crossrefs

Row sums of A339160.
A002218 counts unlabeled 2-connected graphs.
A013922 counts labeled 2-connected graphs.
A322140 is a labeled version.

Extensions

Name changed by Andrew Howroyd, Dec 05 2020
a(11)-a(20) added using geng/multig from nauty by Andrew Howroyd, Dec 05 2020
a(21)-a(23) from Sean A. Irvine, Apr 18 2024
Showing 1-3 of 3 results.