A006443 Number of achiral planar maps with n edges.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• more

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).

Links

• V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.
• Timothy R. Walsh, Number of sensed planar maps with n edges and m vertices, p. 43.
• Nicholas C. Wormald, Counting unrooted planar maps, Discrete Math. 36 (1981), no. 2, 205-225.

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