A006385 Number of unsensed planar maps with n edges. (Formerly M1279)

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

Offset

0,2

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

Table of n, a(n) for n=0..20.

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 [cs.DM], 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.

Formula

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

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.

Sequence in context: A295760 A129876 A038055 * A322859 A183949 A131180

Adjacent sequences: A006382 A006383 A006384 * A006386 A006387 A006388

Keyword

nonn,nice,more

Author

N. J. A. Sloane

Extensions

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

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

Status

approved