A380617 Triangle read by rows: T(n,k) is the number of achiral combinatorial maps with n edges and k vertices, 1 <= k <= n + 1.

1, 1, 1, 2, 2, 1, 5, 8, 5, 2, 16, 28, 26, 12, 3, 53, 121, 128, 82, 28, 6, 206, 528, 686, 505, 239, 68, 10, 817, 2516, 3638, 3192, 1802, 686, 157, 20, 3620, 12302, 20250, 19976, 13268, 6078, 1876, 372, 35, 16361, 63643, 114669, 126876, 95422, 50954, 19346, 5100, 845, 70

Offset

0,4

Comments

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

Links

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

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 |   16,    28,    26,    12,     3;
  5 |   53,   121,   128,    82,    28,    6;
  6 |  206,   528,   686,   505,   239,   68,   10;
  7 |  817,  2516,  3638,  3192,  1802,  686,  157,  20;
  8 | 3620, 12302, 20250, 19976, 13268, 6078, 1876, 372, 35;
  ...

Crossrefs

Row sums are A170947.

Main diagonal is A001405(n-1).

Column 1 is A018191.

Cf. A379431 (planar), A380615 (sensed), A380616 (unsensed).

Sequence in context: A297628 A342722 A344528 * A380616 A380615 A329429

Adjacent sequences: A380614 A380615 A380616 * A380618 A380619 A380620

Keyword

nonn,tabl

Author

Andrew Howroyd, Jan 28 2025

Status

approved