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 A343962 #23 Jun 14 2021 16:01:55 %S A343962 4,14,106,2142,124150,21231450,10794801654,16397345136778, %T A343962 74754715306888786,1026191624073867290710,42506394853041064742716162, %U A343962 5320474615969510569494723118086,2014671515857822813610223858063766522 %N A343962 Number of self-avoiding walks that escape an n X n square lattice starting at a given corner. %C A343962 A self-avoiding walk on a square lattice allows horizontal and vertical movement one step at a time, where no space is visited more than once. %C A343962 The n X n square can be seen as a subset of a larger lattice which surrounds it. Visiting any space on this larger lattice that is not part of the square constitutes escaping the square. %C A343962 There are two ways to escape the square while standing at a corner, and both are counted separately. %C A343962 a(n) is always even due to symmetry along a diagonal. %e A343962 For n=1, every direction will immediately result in escaping the board, so a(1) = 4. %e A343962 For n=2, there are two ways to escape from the starting corner. Otherwise, any of the three remaining corners can be escaped from in two ways, and each corner can be reached from two different directions (clockwise and counterclockwise). Therefore a(2) = 2 + 3*2*2 = 14. %Y A343962 Cf. A341269. %K A343962 nonn,walk,more %O A343962 1,1 %A A343962 _Johan Westin_, May 05 2021 %E A343962 a(7)-a(13) from _Andrew Howroyd_, May 05 2021