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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 (list; graph; refs; listen; history; text; internal format)
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
a(n) = A268553(n) - A357760(n).
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
Sequence in context: A050984 A169686 A184889 * A300147 A087216 A239925
KEYWORD
nonn
AUTHOR
Janaka Rodrigo, Nov 18 2022
STATUS
approved

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Last modified June 13 09:43 EDT 2024. Contains 373383 sequences. (Running on oeis4.)