A378932 Array read by antidiagonals: T(m,n) is the number of minimal edge cuts in the grid graph P_m X P_n.

0, 1, 1, 2, 6, 2, 3, 15, 15, 3, 4, 28, 53, 28, 4, 5, 45, 146, 146, 45, 5, 6, 66, 356, 627, 356, 66, 6, 7, 91, 809, 2471, 2471, 809, 91, 7, 8, 120, 1759, 9292, 16213, 9292, 1759, 120, 8, 9, 153, 3716, 33878, 103196, 103196, 33878, 3716, 153, 9, 10, 190, 7702, 120771, 642364, 1123743, 642364, 120771, 7702, 190, 10

Offset

1,4

Comments

T(m,n) is the number of partitionings of an m X n checkerboard into two edgewise-connected sets.

Links

Table of n, a(n) for n=1..66.

Eric Weisstein's World of Mathematics, Grid Graph.

Eric Weisstein's World of Mathematics, Minimal Edge Cut.

Formula

T(m,n) = T(n,m).

Example

Table starts:
===================================================
m\n | 1  2    3     4      5        6         7 ...
----+----------------------------------------------
  1 | 0  1    2     3      4        5         6 ...
  2 | 1  6   15    28     45       66        91 ...
  3 | 2 15   53   146    356      809      1759 ...
  4 | 3 28  146   627   2471     9292     33878 ...
  5 | 4 45  356  2471  16213   103196    642364 ...
  6 | 5 66  809  9292 103196  1123743  12028981 ...
  7 | 6 91 1759 33878 642364 12028981 221984391 ...
  ...

Crossrefs

Main diagonal is A068416.

Rows 1..4 are A001477(n-1), A000384, A378933, A378934.

Rows 3..8 multiplied by 2 are A166761, A166766, A166769, A166771, A166773, A166774.

Cf. A287151, A359990.

Sequence in context: A334188 A265993 A115009 * A151944 A073094 A388229

Adjacent sequences: A378929 A378930 A378931 * A378933 A378934 A378935

Keyword

nonn,tabl

Author

Andrew Howroyd, Dec 11 2024

Status

approved