A006406 Number of sensed 2-connected simple planar maps with n edges.

1, 1, 2, 4, 9, 24, 81, 274, 1071, 4357, 18416, 80040, 356109, 1610910, 7399114

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn
• more

Comments

A simple planar map is a planar map without loops or parallel edges.

Equivalently, a(n) is the number of embeddings on the sphere of 2-connected planar graphs with n edges up to orientation preserving isomorphisms. - Andrew Howroyd, Mar 27 2021

References

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

Links

• Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.

Crossrefs

Cf. A006402, A006404, A006407 (unsensed case), A342059, A379437 (rooted).

Formula

a(n) = Sum_{k=3..n} A342059(k, n+2-k). - Andrew Howroyd, Mar 27 2021

Extensions

a(11) and a(12) from Sean A. Irvine, Apr 02 2017

a(13)-a(17) from Andrew Howroyd, Mar 27 2021