

A216678


On an n X n grid, number of ways to draw arrows between adjacent nodes such that each node has one outgoing and one incoming arrow, of which the one is not the opposite of the other (i.e., without 2loops).


3



0, 2, 0, 88, 0, 207408, 0, 22902801416, 0, 112398351350823112, 0, 24075116871728596710774372
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OFFSET

1,2


COMMENTS

"Adjacent" is meant in the sense of von Neumann neighborhoods (4 neighbors for "interior" nodes, 3 resp. 2 for nodes on the borders resp. in the corners).
Or: Number of permutations of an n X n array, with each element moving exactly one horizontally or vertically and without 2loops.


LINKS



EXAMPLE

For a 1 X 1 grid, there is no such permutation or possibility.
For a 2 X 2 grid, on has the clockwise and counterclockwise cyclic "permutation" of the 4 nodes. (It is not allowed to draw arrows between 2 pairs of nodes in horizontal or vertical sense since, e.g., the arrow from the first to the second node is the opposite of the arrow from the second to the first node.)
For a 3 X 3 grid, there is no possibility, neither for a 5 X 5 grid.


CROSSREFS

See A216675 for the same problem without the additional restriction.


KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



