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 A249795 #17 Oct 18 2024 11:43:16
%S A249795 1,3,6,12,22,42,78,146,264,490,894,1646,3012,5528,10086,18476,33648,
%T A249795 61472,111702,203552,368872,670538,1213118,2201208,3980380,7214200,
%U A249795 13044916,23627064,42714902,77316682,139695536,252664214,456138008,824332804,1487051098,2685425808
%N A249795 Self-avoiding walks with n steps on the truncated trihexagonal tiling or (4,6,12) lattice.
%C A249795 A self-avoiding walk is a sequence of adjacent points in a lattice that are all distinct.
%C A249795 The truncated trihexagonal tiling or (4,6,12) lattice is one of eight semi-regular tilings of the plane. Each vertex of the lattice is adjacent to a square, hexagon and a 12-sided polygon with sides of equal length.
%C A249795 It is also the Cayley graph of the affine G2 Coxeter group generated by three generators {s_0, s_1, s_2} with the relations (s_0 s_2)^2 = (s_0 s_1)^3 = (s_1 s_2)^6 = 1.
%H A249795 Andrey Zabolotskiy, <a href="/A249795/b249795.txt">Table of n, a(n) for n = 0..47</a> (from Alm, 2005; terms 0..42 from Sean A. Irvine)
%H A249795 Sven Erick Alm, <a href="https://doi.org/10.1088/0305-4470/38/10/001">Upper and lower bounds for the connective constants of self-avoiding walks on the Archimedean and Laves lattices</a>, J. Phys. A.: Math. Gen., 38 (2005), 2055-2080. Also <a href="https://citeseerx.ist.psu.edu/document?doi=17863725272f56f85b6ace259e9b8724f7db96b3">technical report</a> of the same name, 2004. See Table 2, column (4.6.12).
%H A249795 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a249/A249796.java">Java program</a> (github)
%H A249795 Wikipedia, <a href="http://en.wikipedia.org/wiki/Truncated_trihexagonal_tiling">truncated trihexagonal tiling</a>
%e A249795 There are 6 paths of length 2 on the (4,6,12) lattice corresponding to the reduced words in the Coxeter group s_0 s_2, s_0 s_1, s_1 s_2, s_1 s_0, s_2 s_0, s_2 s_1.
%Y A249795 Cf. A001411 (square lattice), A001334 (hexagonal lattice), A249565 (truncated square tiling), A326743 (dual, degree 12 vertex), A326744 (dual, degree 6 vertex), A326745 (dual, degree 4 vertex).
%K A249795 nonn,walk
%O A249795 0,2
%A A249795 _Mike Zabrocki_, Nov 05 2014
%E A249795 a(15)-a(19) corrected by _Mike Zabrocki_ and _Sean A. Irvine_, Jul 25 2019
%E A249795 More terms from _Sean A. Irvine_, Jul 25 2019