A326745 -id:A326745 - cp's OEIS frontend

A249795 Self-avoiding walks with n steps on the truncated trihexagonal tiling or (4,6,12) lattice.

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

Offset: 0

Mike Zabrocki, Nov 05 2014

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.

			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.

Andrey Zabolotskiy, Table of n, a(n) for n = 0..47 (from Alm, 2005; terms 0..42 from Sean A. Irvine)
Sven Erick Alm, Upper and lower bounds for the connective constants of self-avoiding walks on the Archimedean and Laves lattices, J. Phys. A.: Math. Gen., 38 (2005), 2055-2080. Also technical report of the same name, 2004. See Table 2, column (4.6.12).
Sean A. Irvine, Java program (github)
Wikipedia, truncated trihexagonal tiling

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).

a(15)-a(19) corrected by Mike Zabrocki and Sean A. Irvine, Jul 25 2019

More terms from Sean A. Irvine, Jul 25 2019

A326743 Number of length n self-avoiding walks on the kisrhombille tiling starting at a degree 12 vertex.

Original entry on oeis.org

1, 12, 48, 288, 1344, 6828, 32892, 159612, 766356, 3671076, 17521560, 83440932, 396541656, 1881162084, 8909612856, 42136382208, 199020641232, 938971412124, 4425660916764

Offset: 0

Sean A. Irvine, Jul 23 2019

The kisrhombille tiling, Dual(4.6.12), is the dual of the truncated trihexagonal tiling.

Sven Erick Alm, Upper and lower bounds for the connective constants of self-avoiding walks on the Archimedean and Laves lattices, J. Phys. A.: Math. Gen., 38 (2005), 2055-2080. Also technical report of the same name, 2004. See Table 12, column f_1(n).
Sean A. Irvine, Java program (github)
Wikipedia, Kisrhombille tiling

Cf. A326744 (degree 6 vertex), A326745 (degree 4 vertex), A249795 (dual), A298036 (coordination sequence).

a(18) from Alm (2005) added by Andrey Zabolotskiy, Oct 18 2024

A326744 Number of length n self-avoiding walks on the kisrhombille tiling starting at a degree 6 vertex.

Original entry on oeis.org

1, 6, 42, 198, 1068, 5196, 25902, 125874, 609780, 2933562, 14058132, 67139772, 319822572, 1520161374, 7211880744, 34157352042, 161541458514, 763007236542, 3599867690610

Offset: 0

Sean A. Irvine, Jul 23 2019

The kisrhombille tiling, Dual(4.6.12), is the dual of the truncated trihexagonal tiling.

Sven Erick Alm, Upper and lower bounds for the connective constants of self-avoiding walks on the Archimedean and Laves lattices, J. Phys. A.: Math. Gen., 38 (2005), 2055-2080. Also technical report of the same name, 2004. See Table 12, column f_2(n).
Sean A. Irvine, Java program (github)
Wikipedia, Kisrhombille tiling

Cf. A326743 (degree 12 vertex), A326745 (degree 4 vertex), A249795 (dual), A298038 (coordination sequence).

a(18) from Alm (2005) added by Andrey Zabolotskiy, Oct 18 2024

cp's OEIS Frontend

A249795 Self-avoiding walks with n steps on the truncated trihexagonal tiling or (4,6,12) lattice.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A326743 Number of length n self-avoiding walks on the kisrhombille tiling starting at a degree 12 vertex.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A326744 Number of length n self-avoiding walks on the kisrhombille tiling starting at a degree 6 vertex.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions