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 A343310 #27 Feb 16 2025 08:34:02 %S A343310 1,2,4,12,50,264,2054,22324,377704,9455172,385118374,23504746636, %T A343310 2346325946460,348814672315896,84278783653480026,30255270733134656280, %U A343310 17646594353716082850430,15321207204408662854455924,21654163559101840305705453010,45620955950222177660249163228084 %N A343310 a(n) is the number of bilaterally symmetrical self-avoiding paths connecting consecutive corners of an n X n triangular grid. %C A343310 We use unit moves parallel to the triangle edges. %H A343310 Andrew Howroyd, <a href="/A343310/b343310.txt">Table of n, a(n) for n = 1..25</a> %H A343310 Rémy Sigrist, <a href="/A343310/a343310.png">Illustrations of a(5) = 50</a> %H A343310 Rémy Sigrist, <a href="/A343310/a343310.gp.txt">PARI program for A343310</a> %H A343310 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularGridGraph.html">Triangular Grid Graph</a> %H A343310 <a href="/index/Wa#WALKS">Index entries for sequences related to walks</a> %F A343310 a(n) <= A343307(n). %e A343310 For n = 3: %e A343310 - we have the following bilaterally symmetrical paths: %e A343310 . . . . o %e A343310 . / \ %e A343310 . . . o o o---o o o %e A343310 . / \ / \ / \ / \ %e A343310 . o---o---o o o o o . o o . o %e A343310 - so a(3) = 4. %o A343310 (PARI) See Links section. %Y A343310 Cf. A343307. %K A343310 nonn,walk %O A343310 1,2 %A A343310 _Rémy Sigrist_, Apr 11 2021 %E A343310 a(12)-a(13) from _Martin Ehrenstein_, May 02 2021 %E A343310 Terms a(14) and beyond from _Andrew Howroyd_, Feb 05 2022