

A358481


a(n) is the number of different pairs of shortest grid paths joining two opposite corners in opposite order in an n X n X n grid without having middle point on their paths as a common point.


1



30, 6218, 2658432, 1054788750, 552306591900, 269380692717696, 155175092086118400, 83798883891736779150, 50885239237727996887500, 29198209396114625497699068, 18332853214682572877389897728, 10951674446687597386319569942656, 7036938452279110885561897815723264, 4325988198220149508865311059521280000
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OFFSET

1,1


COMMENTS

Alternatively a(n) is the number of ways two ants can interchange their positions starting simultaneously from two opposite corners and moving along shortest grid paths at same speed in an n X n X n grid without meeting other one.


LINKS



FORMULA



EXAMPLE

When n=2 number of ways to move between two opposite corners are given by 6!/(2!*2!*2!) and number of such pairs are given by (6!/(2!*2!*2!))^2. This total number of pairs are given by A268553(2)=8100.
Number of pairs which have the middle point of their paths as a common point are A357760(2)=1782.
Therefore number of pairs without having middle point on their paths as a common point are 81001782=6218


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



