|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,walk
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|