A214816 Number of unsensed combinatorial maps with n edges on an orientable surface of any genus.

1, 2, 5, 20, 96, 644, 5839, 67834, 970568, 16256556, 308620966, 6506035400, 150358570914, 3775903806928, 102348067516576, 2977979542305736, 92579723269733557, 3062602106878957610, 107418879166917701583, 3981908920500346885116, 155550644128029095714786

Offset: 0

Author

N. J. A. Sloane, Jul 31 2012

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..30
• Antonio Breda d'Azevedo, Alexander Mednykh, and Roman Nedela, Enumeration of maps regardless of genus: Geometric approach, Discrete Mathematics, Volume 310, 2010, Pages 1184-1203.
• Timothy R. Walsh, Space-efficient generation of nonisomorphic maps and hypermaps.
• T. R. Walsh, Space-Efficient Generation of Nonisomorphic Maps and Hypermaps, J. Int. Seq. 18 (2015) # 15.4.3.

Crossrefs

Row sums of A379439.

Cf. A006385, A006387, A170946 (sensed), A170947 (achiral), A170948 (chiral pairs), A214814, A214815, A297880, A297881, A348798, A348800, A348801.

Formula

a(n) = (A170946(n) + A170947(n)) / 2. [Breda d'Azevedo, Mednykh & Nedela, Corollary 4.7] - Andrey Zabolotskiy, Jun 06 2024

Extensions

a(12)-a(18) from Andrey Zabolotskiy, Jun 06 2024

a(19) onwards from Andrew Howroyd, Jan 27 2025