

A298022


Coordination sequence for Dual(3^3.4^2) tiling with respect to a trivalent node.


22



1, 3, 7, 12, 17, 23, 28, 33, 37, 42, 47, 51, 56, 61, 65, 70, 75, 79, 84, 89, 93, 98, 103, 107, 112, 117, 121, 126, 131, 135, 140, 145, 149, 154, 159, 163, 168, 173, 177, 182, 187, 191, 196, 201, 205, 210, 215, 219, 224, 229, 233, 238, 243, 247, 252, 257, 261
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OFFSET

0,2


COMMENTS

This tiling is also called the prismatic pentagonal tiling, or the cemd 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. 632640. See Fig. 1 (right).
Tom Karzes, Tiling Coordination Sequences
Reticular Chemistry Structure Resource (RCSR), The cemd 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 GrünbaumShephard 1987 with Anumbers 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(n1) + a(n3)  a(n4) for n>5.
(End)


PROG

(PARI) See Links section.


CROSSREFS

See A298023 for partial sums, A298024 for a tetravalent point.
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.
Sequence in context: A310247 A332263 A310248 * A227133 A170883 A198463
Adjacent sequences: A298019 A298020 A298021 * A298023 A298024 A298025


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Jan 21 2018


EXTENSIONS

More terms from Rémy Sigrist, Jan 21 2018


STATUS

approved



