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 A343307 #22 Feb 16 2025 08:34:02 %S A343307 1,2,10,108,2726,168724,25637074,9454069104,8461610420420, %T A343307 18438745892175008,97929194419509169380,1267379450261470833222676, %U A343307 39964658780097197018058705552,3071011528804416058638501563820092,575150143830631835000028468717331605240 %N A343307 a(n) is the number of self-avoiding paths connecting consecutive corners of an n X n triangular grid. %C A343307 We use unit moves parallel to the triangle edges. %H A343307 Rémy Sigrist, <a href="/A343307/a343307.txt">Python program for A343307</a> %H A343307 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularGridGraph.html">Triangular Grid Graph</a> %H A343307 <a href="/index/Wa#WALKS">Index entries for sequences related to walks</a> %e A343307 For n = 3: %e A343307 - we have the following paths: %e A343307 . . %e A343307 . %e A343307 . . . %e A343307 . %e A343307 . o---o---o %e A343307 . %e A343307 . %e A343307 . . . . %e A343307 . %e A343307 . o . o o . o %e A343307 . / \ / \ / \ / \ %e A343307 . o o---o o o o o---o o %e A343307 . %e A343307 . %e A343307 . . . . %e A343307 . %e A343307 . o---o o---o o---o %e A343307 . / / / \ \ \ %e A343307 . o o---o o . o o---o o %e A343307 . %e A343307 . %e A343307 . o o o %e A343307 . / \ / \ / \ %e A343307 . o o o o o o %e A343307 . / / / \ \ \ %e A343307 . o o---o o . o o---o o %e A343307 - so a(3) = 10. %o A343307 (Python) # See Links section. %Y A343307 Cf. A007764, A112675, A288148, A308144, A343310. %K A343307 nonn,walk,hard %O A343307 1,2 %A A343307 _Rémy Sigrist_, Apr 11 2021 %E A343307 a(14)-a(15) from _Andrew Howroyd_, Feb 04 2022