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 A323562 #25 Jul 24 2020 01:44:37 %S A323562 8,200,2446,21946,169782,1205428,8119338,52862872,336465352,2108185746 %N A323562 Number of rooted self-avoiding king's walks on an infinite chessboard trapped after n moves. %C A323562 The first step is either (0,0)->(1,0) or (0,0)->(1,1). Rotated paths are not counted separately. %C A323562 The average number of moves of a self-avoiding random walk of a king on an infinite chessboard to self-trapping is 209.71. The corresponding number of moves for paths with forbidden crossing (A323141) is 69.865. %C A323562 a(n)=0 for n<8. %H A323562 Hugo Pfoertner, <a href="/A323562/a323562.pdf">Probability density for the number of moves to self-trapping</a>, (2019). %e A323562 a(8) = 8, because the following 8 walks of 8 moves of a king starting at S with a first move (0,0)->(1,0) visit all neighbors of the trapping location T. The starting point itself is also blocked. There are no such shortest walks with first move (0,0)->(1,1). %e A323562 . %e A323562 o <-- o <-- o o o <-- o o --> o --> o o <-- o <-- o %e A323562 | ^ ^ \ / ^ ^ | | ^ %e A323562 v | | / \ | | v v | %e A323562 o --> T o o T o o T o o T o %e A323562 ^ ^ \ \ | | / ^ %e A323562 | | \ \ v v / | %e A323562 S --> o --> o S --> o --> o S --> o o o S --> o %e A323562 . %e A323562 S --> o --> o S --> o --> o S --> o o o S --> o %e A323562 | | / / ^ ^ \ | %e A323562 v v / / | | \ v %e A323562 o --> T o o T o o T o o T o %e A323562 ^ | | \ / | | ^ ^ | %e A323562 | v v / \ v v | | v %e A323562 o <-- o <-- o o o <-- o o --> o --> o o <-- o <-- o %e A323562 - _Hugo Pfoertner_, Jul 23 2020 %Y A323562 Cf. A077482, A322831, A323141, A323560, A323561. %K A323562 nonn,walk,more %O A323562 8,1 %A A323562 _Hugo Pfoertner_, Jan 17 2019