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A380234 Triangle read by rows: T(n,k) is the number of achiral combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).

%I A380234 #7 Jan 17 2025 12:16:02
%S A380234 1,2,4,1,14,6,47,34,4,184,188,46,761,1040,408,33,3314,5756,3220,538,
%T A380234 14997,32069,23824,6489,398,69886,179408,169336,66150,8506,333884,
%U A380234 1009234,1170654,611278,129030,6405,1626998,5700548,7930892,5279172,1608172,168702,8067786,32341002,52930196,43429578,17758601,3080190,128448
%N A380234 Triangle read by rows: T(n,k) is the number of achiral combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).
%C A380234 Achiral maps are also called reflexible.
%H A380234 Andrew Howroyd, <a href="/A380234/b380234.txt">Table of n, a(n) for n = 0..120</a> (rows 0..20)
%H A380234 Evgeniy Krasko and Alexander Omelchenko, <a href="https://arxiv.org/abs/1712.10139">Enumeration of Unsensed Orientable Maps on Surfaces of a Given Genus</a>, arXiv:1712.10139 [math.CO], 2017.
%H A380234 Evgeniy Krasko, <a href="https://github.com/krasko/reflexible_maps/blob/master/G_0_to_10.txt">Reflexible maps with E edges on orientable surfaces of genus G</a>, 2017 (data file).
%e A380234 Triangle starts:
%e A380234   n\k    [0]     [1]     [2]    [3]   [4]
%e A380234   [0]     1;
%e A380234   [1]     2;
%e A380234   [2]     4,      1;
%e A380234   [3]    14,      6;
%e A380234   [4]    47,     34,      4;
%e A380234   [5]   184,    188,     46;
%e A380234   [6]   761,   1040,    408,    33;
%e A380234   [7]  3314,   5756,   3220,   538;
%e A380234   [8] 14997,  32069,  23824,  6489,  398;
%e A380234   [9] 69886, 179408, 169336, 66150, 8506;
%e A380234   ...
%Y A380234 Row sums are A170947.
%Y A380234 Column 0 is A006443.
%Y A380234 Cf. A379438 (sensed), A379439 (unsensed).
%K A380234 nonn,tabf
%O A380234 0,2
%A A380234 _Andrew Howroyd_, Jan 17 2025