A324604 - OEIS

%I #20 Oct 28 2021 07:10:50

%S 2,2,4,2,7,22,2,13,66,258,2,25,189,898,3528,2,49,537,3118,14545,87830,

%T 2,97,1544,11462,75446,746589,8295536,2,193,4508,44990,447667

%N Table read by rows: T(n,k) is the number of non-intersecting loops starting at (0,0) on the n X k torus consisting of steps up and to the right, 1 <= k <= n.

%C Conjecture: Second column is A181565.

%H Peter Kagey, <a href="https://codegolf.stackexchange.com/q/181203/53884">Cycles on the torus</a>, Programming Puzzles & Code Golf Stack Exchange.

%e The T(3,2) = 7 walks on the 3 X 2 torus are:

%e   (0,0),(0,1),(0,0)

%e   (0,0),(1,0),(2,0),(0,0)

%e   (0,0),(0,1),(1,1),(1,0),(2,0),(0,0)

%e   (0,0),(0,1),(1,1),(2,1),(2,0),(0,0)

%e   (0,0),(1,0),(1,1),(2,1),(0,1),(0,0)

%e   (0,0),(1,0),(1,1),(2,1),(2,0),(0,0)

%e   (0,0),(1,0),(2,0),(2,1),(0,1),(0,0)

%e Table begins:

%e   2

%e   2,  4,

%e   2,  7,   22,

%e   2, 13,   66,   258,

%e   2, 25,  189,   898,  3528,

%e   2, 49,  537,  3118, 14545,  87830,

%e   2, 97, 1544, 11462, 75446, 746589, 8295536

%Y Cf. A181565, A324603.

%K tabl,more,nonn,walk

%O 1,1

%A _Peter Kagey_, Mar 09 2019