A326745 - OEIS

%I #10 Oct 18 2024 11:43:20

%S 1,4,32,160,852,4232,21020,102652,497720,2397844,11501012,54967576,

%T 261998092,1245969948,5913866044,28021308344,132570243968,

%U 626365075348,2956008677160

%N Number of length n self-avoiding walks on the kisrhombille tiling starting at a degree 4 vertex.

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

%H Sven Erick Alm, <a href="https://doi.org/10.1088/0305-4470/38/10/001">Upper and lower bounds for the connective constants of self-avoiding walks on the Archimedean and Laves lattices</a>, J. Phys. A.: Math. Gen., 38 (2005), 2055-2080. Also <a href="https://citeseerx.ist.psu.edu/document?doi=17863725272f56f85b6ace259e9b8724f7db96b3">technical report</a> of the same name, 2004. See Table 12, column f_3(n).

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a326/A326745.java">Java program</a> (github)

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Truncated_trihexagonal_tiling#Kisrhombille_tiling">Kisrhombille tiling</a>

%Y Cf. A326743 (degree 12 vertex), A326744 (degree 6 vertex), A249795 (dual), A298040 (coordination sequence).

%K nonn,walk,more

%O 0,2

%A _Sean A. Irvine_, Jul 23 2019

%E a(18) from Alm (2005) added by _Andrey Zabolotskiy_, Oct 18 2024