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

0,2

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.

Formula

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

Example

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;

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.

Sequence in context: A184176 A163546 A380234 * A379438 A172385 A081538

Adjacent sequences: A379436 A379437 A379438 * A379442 A379443 A379444

Keyword

nonn,tabf

Author

Andrew Howroyd, Jan 16 2025

Status

approved