A379431 Array read by antidiagonals: A(n,k) is the number of achiral planar maps with n vertices and k faces, n >= 1, k >= 1.

1, 1, 1, 1, 2, 1, 2, 5, 5, 2, 3, 12, 17, 12, 3, 6, 28, 58, 58, 28, 6, 10, 68, 179, 247, 179, 68, 10, 20, 157, 538, 942, 942, 538, 157, 20, 35, 372, 1531, 3388, 4345, 3388, 1531, 372, 35, 70, 845, 4288, 11424, 18316, 18316, 11424, 4288, 845, 70

Offset

1,5

Comments

The planar maps considered are connected and may contain loops and parallel edges.

The number of edges is n + k - 2.

Links

Table of n, a(n) for n=1..55.

Formula

A(n,k) = A(k,n).

Example

==================================================
n\k |  1   2    3     4     5     6     7    8 ...
----+---------------------------------------------
  1 |  1   1    1     2     3     6    10   20 ...
  2 |  1   2    5    12    28    68   157  372 ...
  3 |  1   5   17    58   179   538  1531 4288 ...
  4 |  2  12   58   247   942  3388 11424 ...
  5 |  3  28  179   942  4345 18316 ...
  6 |  6  68  538  3388 18316 ...
  7 | 10 157 1531 11424 ...
  8 | 20 372 4288 ...
  ...
As a triangle, rows give the number of edges (first row is 0 edges):
   1;
   1,   1;
   1,   2,    1;
   2,   5,    5,   2;
   3,  12,   17,   12,    3;
   6,  28,   58,   58,   28,    6;
  10,  68,  179,  247,  179,   68,   10;
  20, 157,  538,  942,  942,  538,  157,  20;
  35, 372, 1531, 3388, 4345, 3388, 1531, 372, 35;
  ...

Crossrefs

Antidiagonal sums are A006443.

Column 1 is A210736(n-1).

Cf. A269920 (rooted), A277741 (unsensed), A379430 (sensed).

Sequence in context: A143913 A228815 A241555 * A277741 A379430 A241138

Adjacent sequences: A379428 A379429 A379430 * A379432 A379433 A379434

Keyword

nonn,tabl

Author

Andrew Howroyd, Jan 14 2025

Status

approved