A006385 Number of unsensed planar maps with n edges.

1, 2, 4, 14, 52, 248, 1416, 9172, 66366, 518868, 4301350, 37230364, 333058463, 3057319072, 28656583950, 273298352168, 2645186193457, 25931472185976, 257086490694917, 2574370590192556, 26010904915620261

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• more

Comments

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).
• T. R. S. Walsh, personal communication.

Links

• Richard Kapolnai, Gabor Domokos, and Timea Szabo, Generating spherical multiquadrangulations by restricted vertex splittings and the reducibility of equilibrium classes, Periodica Polytechnica Electrical Engineering, 56(1):11-10, 2012. Also arXiv:1206.1698, 2012. See Table 2.
• Valery. A. Liskovets, A reductive technique for enumerating nonisomorphic planar maps, Discr. Math., v.156 (1996), 197-217.
• Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.
• Timothy R. Walsh, Space-efficient generation of nonisomorphic maps and hypermaps
• Timothy R. Walsh, Space-Efficient Generation of Nonisomorphic Maps and Hypermaps, J. Int. Seq. 18 (2015) # 15.4.3
• Nicholas C. Wormald, Counting unrooted planar maps, Discrete Math. 36 (1981), no. 2, 205-225.

Crossrefs

Antidiagonal sums of A277741.

Column k=0 of A379439.

Cf. A000168 (rooted), A006384 (sensed), A006443 (achiral), A006403 (2-connected), A090376.

Cf. A006387 (genus 1), A214814 (genus 2), A214815 (genus 3), A214816.

Formula

a(n) = (A006384(n) + A006443(n))/2. - Andrew Howroyd, Jan 13 2025

Extensions

a(18)-a(19) added by Andrew Howroyd, Jan 13 2025

a(20) added by Andrew Howroyd, Jan 20 2025