cp's OEIS Frontend

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.

%I A358481 #8 Dec 21 2022 12:03:07
%S A358481 30,6218,2658432,1054788750,552306591900,269380692717696,
%T A358481 155175092086118400,83798883891736779150,50885239237727996887500,
%U A358481 29198209396114625497699068,18332853214682572877389897728,10951674446687597386319569942656,7036938452279110885561897815723264,4325988198220149508865311059521280000
%N 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.
%C A358481 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.
%F A358481 a(n) = A268553(n) - A357760(n).
%e A358481 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.
%e A358481 Number of pairs which have the middle point of their paths as a common point are A357760(2)=1782.
%e A358481 Therefore number of pairs without having middle point on their paths as a common point are 8100-1782=6218
%Y A358481 Cf. A268553, A357760.
%K A358481 nonn
%O A358481 1,1
%A A358481 _Janaka Rodrigo_, Nov 18 2022