A380616 Triangle read by rows: T(n,k) is the number of unsensed combinatorial maps with n edges and k vertices, 1 <= k <= n + 1.

1, 1, 1, 2, 2, 1, 5, 8, 5, 2, 17, 33, 30, 13, 3, 79, 198, 208, 118, 35, 6, 554, 1571, 1894, 1232, 472, 104, 12, 5283, 16431, 21440, 15545, 6879, 1914, 315, 27, 65346, 213831, 296952, 233027, 115134, 37311, 7881, 1021, 65, 966156, 3288821, 4799336, 4019360, 2163112, 787065, 196267, 32857, 3407, 175

Offset

0,4

Comments

By duality, also the number of unsensed combinatorial maps with n edges and k faces.

Links

Table of n, a(n) for n=0..54.

Formula

T(n,k) = (A380615(n,k) + A380617(n,k))/2.

Example

Triangle begins:
n\k |     1       2       3       4       5      6     7     8   9
----+--------------------------------------------------------------
  0 |     1;
  1 |     1,      1;
  2 |     2,      2,      1;
  3 |     5,      8,      5,      2;
  4 |    17,     33,     30,     13,      3;
  5 |    79,    198,    208,    118,     35,     6;
  6 |   554,   1571,   1894,   1232,    472,   104,   12;
  7 |  5283,  16431,  21440,  15545,   6879,  1914,  315,   27;
  8 | 65346, 213831, 296952, 233027, 115134, 37311, 7881, 1021, 65;
  ...

Crossrefs

Row sums are A214816.

Main diagonal is A006082(n+1).

Columns 1..3 are A054499, A380620, A380621.

Cf. A053979 (rooted), A277741 (planar), A380615 (sensed), A380617 (achiral).

Sequence in context: A342722 A344528 A380617 * A380615 A329429 A326617

Adjacent sequences: A380613 A380614 A380615 * A380617 A380618 A380619

Keyword

nonn,tabl

Author

Andrew Howroyd, Jan 28 2025

Status

approved