

A298038


Coordination sequence of Dual(4.6.12) tiling with respect to a hexavalent node.


23



1, 6, 24, 18, 48, 30, 72, 42, 96, 54, 120, 66, 144, 78, 168, 90, 192, 102, 216, 114, 240, 126, 264, 138, 288, 150, 312, 162, 336, 174, 360, 186, 384, 198, 408, 210, 432, 222, 456, 234, 480, 246, 504, 258, 528, 270, 552, 282, 576, 294, 600, 306, 624, 318, 648
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OFFSET

0,2


COMMENTS

Conjecture: For n > 0, a(n)=12n if n even, otherwise 6n.


LINKS

Table of n, a(n) for n=0..54.
Tom Karzes, Tiling Coordination Sequences
N. J. A. Sloane, Illustration of initial terms (shows one 60degree sector of tiling)
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]


FORMULA

Conjectures from Colin Barker, Apr 03 2020: (Start)
G.f.: (1 + 6*x + 22*x^2 + 6*x^3 + x^4) / ((1  x)^2*(1 + x)^2).
a(n) = 2*a(n2)  a(n4) for n>4.
(End)


CROSSREFS

Cf. A072154, A298039 (partial sums), A298036 (12valent node), A298040 (tetravalent node).
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: A112034 A327568 A280589 * A223751 A228745 A049319
Adjacent sequences: A298035 A298036 A298037 * A298039 A298040 A298041


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Jan 22 2018


EXTENSIONS

Terms a(8)a(54) added by Tom Karzes, Apr 01 2020


STATUS

approved



