A379439 Triangle read by rows: T(n,k) is the number of unsensed combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).

1, 2, 4, 1, 14, 6, 52, 40, 4, 248, 320, 76, 1416, 2946, 1395, 82, 9172, 29364, 24950, 4348, 66366, 309558, 427336, 160050, 7258, 518868, 3365108, 6987100, 4696504, 688976, 4301350, 37246245, 109761827, 118353618, 37466297, 1491629, 37230364, 416751008, 1668376886, 2675297588, 1512650776, 195728778

Offset: 0

Author

Andrew Howroyd, Jan 16 2025

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  n\k     [0]      [1]      [2]      [3]     [4]
  [0]      1;
  [1]      2;
  [2]      4,       1;
  [3]     14,       6;
  [4]     52,      40,       4;
  [5]    248,     320,      76;
  [6]   1416,    2946,    1395,      82;
  [7]   9172,   29364,   24950,    4348;
  [8]  66366,  309558,  427336,  160050,   7258;
  [9] 518868, 3365108, 6987100, 4696504, 688976;
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..120 (rows 0..20)
• Evgeniy Krasko and Alexander Omelchenko, Enumeration of Unsensed Orientable Maps on Surfaces of a Given Genus, arXiv:1712.10139 [math.CO], 2017, see Appendix Table 4.

Crossrefs

Row sums are A214816.

Columns 0..8 are A006385, A006387, A214814, A214815, A297880, A297881, A348798, A348800, A348801.

Cf. A269919 (rooted), A379438 (sensed), A380234 (achiral), A380235.

Formula

T(n,k) = (A379438(n,k) + A380234(n,k))/2.