

A249795


Selfavoiding 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
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OFFSET

0,2


COMMENTS

A selfavoiding 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 semiregular tilings of the plane. Each vertex of the lattice is adjacent to a square, hexagon and a 12sided 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



