A006386 Number of sensed genus 1 maps with n edges.

1, 6, 46, 452, 4852, 52972, 587047, 6550808, 73483256, 827801468, 9360123740, 106189359544, 1208328304864, 13787042250528, 157700137398689, 1807893066408464, 20768681225892328, 239037464947999900, 2755989928117365244, 31826208029615881656, 368074022535205870382

Offset: 2

Author

N. J. A. Sloane

Keywords

• nice
• nonn

Comments

A genus 1 map can be called a toroidal map.

References

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

Links

• T. D. Noe, Table of n, a(n) for n = 2..30 (from Mednykh and Nedela)
• A. D. Mednykh and R. Nedela, Enumeration of unrooted maps with given genus, J. Combin. Th. B, 96 (2006), 706-729.
• Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.
• Timothy R. Walsh, Counting maps on doughnuts, Theoretical Computer Science, vol.502, pp.4-15, (September-2013).
• Timothy R. S. Walsh, Alain Giorgetti, Alexander Mednykh, Enumeration of unrooted orientable maps of arbitrary genus by number of edges and vertices, Discrete Math. 312 (2012), no. 17, 2660--2671. MR2935417. - From _N. J. A. Sloane_, Aug 01 2012

Crossrefs

Column k=1 of A379438.

Cf. A006300 (rooted), A006384 (planar), A006387 (unsensed), A104595, A104596, A215019.

Extensions

More terms from Valery A. Liskovets, Mar 22 2005

Edited by N. J. A. Sloane, May 23 2008