This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A324603 #19 Dec 15 2024 15:35:07 %S A324603 2,4,22,258,3528,87830,8295536 %N A324603 Number of non-intersecting loops starting at (0,0) on the n X n torus consisting of steps up and to the right. %H A324603 Peter Kagey, <a href="https://codegolf.stackexchange.com/q/181203/53884">Cycles on the torus</a>, Programming Puzzles & Code Golf Stack Exchange. %e A324603 On the 2 X 2 torus, the 4 walks are: %e A324603 [(0,0),(1,0),(0,0)] %e A324603 [(0,0),(0,1),(0,0)] %e A324603 [(0,0),(0,1),(1,1),(1,0),(0,0)] %e A324603 [(0,0),(1,0),(1,1),(0,1),(0,0)] %e A324603 On the 3 X 3 torus, the 22 walks are all equivalent to the following eleven walks by switching coordinates: %e A324603 [(0,0),(0,1),(0,2),(0,0)] %e A324603 [(0,0),(0,1),(1,1),(2,1),(2,2),(0,2),(0,0)] %e A324603 [(0,0),(0,1),(1,1),(2,1),(2,2),(2,0),(0,0)] %e A324603 [(0,0),(0,1),(1,1),(1,2),(2,2),(0,2),(0,0)] %e A324603 [(0,0),(0,1),(1,1),(1,2),(2,2),(2,0),(0,0)] %e A324603 [(0,0),(0,1),(1,1),(1,2),(1,0),(2,0),(0,0)] %e A324603 [(0,0),(0,1),(0,2),(1,2),(2,2),(2,0),(0,0)] %e A324603 [(0,0),(0,1),(0,2),(1,2),(1,0),(2,0),(0,0)] %e A324603 [(0,0),(0,1),(1,1),(2,1),(2,2),(0,2),(1,2),(1,0),(2,0),(0,0)] %e A324603 [(0,0),(0,1),(1,1),(1,2),(1,0),(2,0),(2,1),(2,2),(0,2),(0,0)] %e A324603 [(0,0),(0,1),(0,2),(1,2),(1,0),(1,1),(2,1),(2,2),(2,0),(0,0)] %Y A324603 Cf. A000984, A324604. %K A324603 nonn,more,walk %O A324603 1,1 %A A324603 _Peter Kagey_, Mar 09 2019