A360444 a(n) is the number of ways for two nonintersecting, unordered pairs of shortest grid paths to cross over between two opposite corners in an n X n grid without intersecting opposite paths at their middle points.

0, 0, 52, 4540, 742404, 103625004, 16451015760, 2693403573732, 463439672732740, 82516389937797244, 15153421065014201424, 2855078861978328905660, 550005952989718178915472, 108007620360200608500699120, 21569526154939330279935568704

Offset

1,3

Comments

Alternatively, the number of different ways when two of four ants start at one corner of the grid and other two start at the opposite corner at the same time t and they all stop moving at time T (at which time each ant reaches the corner opposite from its starting corner) and at no time in the open interval (t,T) does any ant meet any other ant.

Links

Table of n, a(n) for n=1..15.

Example

In the 1 X 1 and 2 X 2 grids there is no possibility of this happening.
In a 3 X 3 grid, if a pair starting from the bottom left corner move along NNNEEE and EEENNN, the pair starting from the top right corner can move along WWSWSS and SSWSWW (this is only one of the nine options available for the second pair) so that they can cross over without meeting any other. There are 52 different ways to do this.

Crossrefs

Cf. A362207, A358481, A357760, A357603, A000891.

Sequence in context: A042301 A156854 A282590 * A027550 A006179 A029809

Adjacent sequences: A360441 A360442 A360443 * A360445 A360446 A360447

Keyword

nonn

Author

Janaka Rodrigo, Jul 15 2023

Status

approved