OFFSET
0,2
COMMENTS
This tiling is also called the prismatic pentagonal tiling, or the cem-d net. It is one of the 11 Laves tilings.
REFERENCES
B. Gruenbaum and G. C. Shephard, Tilings and Patterns, W. H. Freeman, New York, 1987. See p. 96.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..1000
Chung, Ping Ngai, Miguel A. Fernandez, Yifei Li, Michael Mara, Frank Morgan, Isamar Rosa Plata, Niralee Shah, Luis Sordo Vieira, and Elena Wikner. Isoperimetric Pentagonal Tilings, Notices of the AMS 59, no. 5 (2012), pp. 632-640. See Fig. 1 (right).
Tom Karzes, Tiling Coordination Sequences
Frank Morgan, Optimal Pentagonal Tilings, Video, May 2021 [Mentions this tiling
Reticular Chemistry Structure Resource (RCSR), The cem-d tiling (or net)
Rémy Sigrist, PARI program for A298022
N. J. A. Sloane, Overview of coordination sequences of Laves tilings [Fig. 2.7.1 of Grünbaum-Shephard 1987 with A-numbers added and in some cases the name in the RCSR database]
N. J. A. Sloane, Illustration of initial terms
FORMULA
Conjectures from Colin Barker, Jan 22 2018: (Start)
G.f.: (1 + 2*x + 4*x^2 + 4*x^3 + 3*x^4 + 2*x^5 - 2*x^8) / ((1 - x)^2*(1 + x + x^2)).
a(n) = a(n-1) + a(n-3) - a(n-4) for n>5.
(End)
PROG
(PARI) See Links section.
CROSSREFS
List of coordination sequences for Laves tilings (or duals of uniform planar nets): [3,3,3,3,3.3] = A008486; [3.3.3.3.6] = A298014, A298015, A298016; [3.3.3.4.4] = A298022, A298024; [3.3.4.3.4] = A008574, A296368; [3.6.3.6] = A298026, A298028; [3.4.6.4] = A298029, A298031, A298033; [3.12.12] = A019557, A298035; [4.4.4.4] = A008574; [4.6.12] = A298036, A298038, A298040; [4.8.8] = A022144, A234275; [6.6.6] = A008458.
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 21 2018
EXTENSIONS
More terms from Rémy Sigrist, Jan 21 2018
STATUS
approved