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 A249795 Self-avoiding walks with n steps on the truncated trihexagonal tiling or (4,6,12) lattice. 4
 1, 3, 6, 12, 22, 42, 78, 146, 264, 490, 894, 1646, 3012, 5528, 10086, 18476, 33648, 61472, 111702, 203552, 368872, 670538, 1213118, 2201208, 3980380, 7214200, 13044916, 23627064, 42714902, 77316682, 139695536, 252664214, 456138008, 824332804, 1487051098, 2685425808 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A self-avoiding walk is a sequence of adjacent points in a lattice that are all distinct. 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. 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. LINKS Sean A. Irvine, Table of n, a(n) for n = 0..42 Sean A. Irvine, Java program (github) Wikipedia, truncated trihexagonal tiling EXAMPLE 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. CROSSREFS 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). Sequence in context: A288348 A018078 A005404 * A097939 A249565 A174201 Adjacent sequences:  A249792 A249793 A249794 * A249796 A249797 A249798 KEYWORD nonn,walk AUTHOR Mike Zabrocki, Nov 05 2014 EXTENSIONS a(15)-a(19) corrected by Mike Zabrocki and Sean A. Irvine, Jul 25 2019 More terms from Sean A. Irvine, Jul 25 2019 STATUS approved

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Last modified October 30 03:24 EDT 2020. Contains 338076 sequences. (Running on oeis4.)