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%I #15 May 02 2019 20:37:52
%S 2,4,22,258,3528,87830,8295536
%N Number of non-intersecting loops starting at (0,0) on the n X n torus consisting of steps up and to the right.
%C On the 2 X 2 torus, the 4 walks are:
%C [(0,0),(1,0),(0,0)]
%C [(0,0),(0,1),(0,0)]
%C [(0,0),(0,1),(1,1),(1,0),(0,0)]
%C [(0,0),(1,0),(1,1),(0,1),(0,0)]
%C On the 3 X 3 torus, the 22 walks are all equivalent to the following eleven walks by switching coordinates:
%C [(0,0),(0,1),(0,2),(0,0)]
%C [(0,0),(0,1),(1,1),(2,1),(2,2),(0,2),(0,0)]
%C [(0,0),(0,1),(1,1),(2,1),(2,2),(2,0),(0,0)]
%C [(0,0),(0,1),(1,1),(1,2),(2,2),(0,2),(0,0)]
%C [(0,0),(0,1),(1,1),(1,2),(2,2),(2,0),(0,0)]
%C [(0,0),(0,1),(1,1),(1,2),(1,0),(2,0),(0,0)]
%C [(0,0),(0,1),(0,2),(1,2),(2,2),(2,0),(0,0)]
%C [(0,0),(0,1),(0,2),(1,2),(1,0),(2,0),(0,0)]
%C [(0,0),(0,1),(1,1),(2,1),(2,2),(0,2),(1,2),(1,0),(2,0),(0,0)]
%C [(0,0),(0,1),(1,1),(1,2),(1,0),(2,0),(2,1),(2,2),(0,2),(0,0)]
%C [(0,0),(0,1),(0,2),(1,2),(1,0),(1,1),(2,1),(2,2),(2,0),(0,0]]
%H Peter Kagey, <a href="https://codegolf.stackexchange.com/q/181203/53884">Cycles on the torus</a>, Programming Puzzles & Code Golf Stack Exchange.
%Y Cf. A000984, A324604.
%K nonn,more,walk
%O 1,1
%A _Peter Kagey_, Mar 09 2019
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