

A298015


Coordination sequence of snub632 tiling with respect to a trivalent node of type shortshortshort.


22



1, 3, 6, 15, 21, 18, 33, 48, 30, 51, 72, 42, 69, 96, 54, 87, 120, 66, 105, 144, 78, 123, 168, 90, 141, 192, 102, 159, 216, 114, 177, 240, 126, 195, 264, 138, 213, 288, 150, 231, 312, 162, 249, 336, 174, 267, 360, 186, 285, 384, 198, 303, 408, 210, 321, 432, 222, 339, 456, 234, 357, 480, 246, 375
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OFFSET

0,2


COMMENTS

The snub632 tiling in also called the fszd net. It is the dual of the 3.3.3.3.6 Archimedean tiling.
This is also called the "6fold pentille" tiling in Conway, Burgiel, GoodmanStrauss, 2008, p. 288.  Felix Fröhlich, Jan 13 2018


REFERENCES

J. H. Conway, H. Burgiel and Chaim GoodmanStrauss, The Symmetries of Things, A K Peters, Ltd., 2008, ISBN 9781568812205.


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
Chaim GoodmanStrauss and N. J. A. Sloane, A Coloring Book Approach to Finding Coordination Sequences, Acta Cryst. A75 (2019), 121134, also on NJAS's home page. Also arXiv:1803.08530. [Warning: there is an error in Eq. 8(b), the a(4) term should be changed from 24 to 21. With that correction Theorem then still holds.  N. J. A. Sloane, Apr 01 2020]
Tom Karzes, Illustration of a(0) to a(4) [Key: n, a(n), color: 0, 1, green; 1, 3, red; 2, 6, blue; 3, 15, purple; 4, 21, beige.]
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]
Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,1).


FORMULA

For n >= 6, let k=floor(n/3), so k >= 2. Then a(3*k) = 18*k3, a(3*k+1)=24*k, a(3*k+2)=12*k+6. [Corrected by N. J. A. Sloane, Apr 01 2020]
a(n) = 2*a(n3)  a(n6) for n>=11. [Corrected by N. J. A. Sloane, Apr 01 2020]
G.f.: (3*x^109*x^74*x^66*x^515*x^413*x^36*x^23*x1)/(x^62*x^3+1). [Corrected by N. J. A. Sloane, Apr 01 2020]


CROSSREFS

Cf. A298014, A298016.
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: A162335 A289296 A310126 * A256906 A095869 A292610
Adjacent sequences: A298012 A298013 A298014 * A298016 A298017 A298018


KEYWORD

nonn,easy


AUTHOR

Chaim GoodmanStrauss and N. J. A. Sloane, Jan 11 2018


EXTENSIONS

a(4) corrected by Tom Karzes. I corrected the bfile and the formulas and deleted the programs.  N. J. A. Sloane, Apr 01 2020


STATUS

approved



