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.
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 8100-1782=6218
CROSSREFS
KEYWORD
nonn
AUTHOR
Janaka Rodrigo, Nov 18 2022
STATUS
approved