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Number of unsensed combinatorial maps with n edges on an orientable surface of any genus.
13

%I #21 Jan 27 2025 14:27:39

%S 1,2,5,20,96,644,5839,67834,970568,16256556,308620966,6506035400,

%T 150358570914,3775903806928,102348067516576,2977979542305736,

%U 92579723269733557,3062602106878957610,107418879166917701583,3981908920500346885116,155550644128029095714786

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

%H Andrew Howroyd, <a href="/A214816/b214816.txt">Table of n, a(n) for n = 0..30</a>

%H Antonio Breda d'Azevedo, Alexander Mednykh, and Roman Nedela, <a href="https://doi.org/10.1016/j.disc.2009.11.017">Enumeration of maps regardless of genus: Geometric approach</a>, Discrete Mathematics, Volume 310, 2010, Pages 1184-1203.

%H Timothy R. Walsh, <a href="http://www.info2.uqam.ca/~walsh_t/papers/GENERATING NONISOMORPHIC.pdf">Space-efficient generation of nonisomorphic maps and hypermaps</a>.

%H T. R. Walsh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Walsh/walsh3.html">Space-Efficient Generation of Nonisomorphic Maps and Hypermaps</a>, J. Int. Seq. 18 (2015) # 15.4.3.

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

%Y Row sums of A379439.

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

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jul 31 2012

%E a(12)-a(18) from _Andrey Zabolotskiy_, Jun 06 2024

%E a(19) onwards from _Andrew Howroyd_, Jan 27 2025