A006386 Number of sensed genus 1 maps with n edges. (Formerly M4253)

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

Offset

2,2

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.

Sequence in context: A218497 A261499 A001829 * A326324 A215084 A232058

Adjacent sequences: A006383 A006384 A006385 * A006387 A006388 A006389

Keyword

nice,nonn

Author

N. J. A. Sloane

Extensions

More terms from Valery A. Liskovets, Mar 22 2005

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

Status

approved