OEIS/Tilings

Generating functions of coordination sequences

• Brian Galebach, k-uniform tilings (k <= 6) and their A-numbers
• Chaim Goodman-Strauss and N. J. A. Sloane, ">A Coloring Book Approach to Finding Coordination Sequences, Acta Cryst. A75 (2019), 121-134, also on NJAS's home page. Also " arXiv:1803.08530.
• M.[ichael P.] Benson, Growth series of finite extensions of Zn are rational, Invent. Math. 73 (1983), no. 2, 251–269. MR 714092
• Branko Grunbaum and Geoffrey C. Shephard, Tilings by Regular Polygons, Mathematics Magazine, Vol. 50, No. 5 (Nov., 1977), pp. 227-247
• Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites after Grosse-Kunstleve, Brunner, and Sloane (with coefficients of many g.f.s)
• R. W. Grosse-Kunstleve, G. O. Brunner, and N. J. A. Sloane, Algebraic description of coordination sequences and exact topological densities for zeolites. Acta Cryst., A52:879–889, 1996.

New format

This encoding uses uppercase and lowercase letters only. k-uniformity is encoded by chr(ord('A') - 1 + k). The possible vertex types are encoded as follows:

A: 3.3.3.3.3.3
B: 3.3.3.3.6
C: 3.3.3.4.4
D: 3.3.4.3.4
E: 3.3.4.12
F: 3.3.6.6
G: 3.4.3.12
H: 3.4.4.6
I: 3.4.6.4
J: 3.6.3.6
K: 3.12.12
L: 4.4.4.4
M: 4.6.12
N: 4.8.8
O: 6.6.6

Corresponding lowercase letters are used if the orientation of the target vertex is opposite to the orientation of the focus vertex.