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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.)