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%I #28 Apr 04 2020 01:35:31
%S 1,6,24,18,48,30,72,42,96,54,120,66,144,78,168,90,192,102,216,114,240,
%T 126,264,138,288,150,312,162,336,174,360,186,384,198,408,210,432,222,
%U 456,234,480,246,504,258,528,270,552,282,576,294,600,306,624,318,648
%N Coordination sequence of Dual(4.6.12) tiling with respect to a hexavalent node.
%C Conjecture: For n > 0, a(n)=12n if n even, otherwise 6n.
%H Tom Karzes, <a href="/A250122/a250122.html">Tiling Coordination Sequences</a>
%H N. J. A. Sloane, <a href="/A298036/a298038.png">Illustration of initial terms</a> (shows one 60-degree sector of tiling)
%H N. J. A. Sloane, <a href="/A296368/a296368_2.png">Overview of coordination sequences of Laves tilings</a> [Fig. 2.7.1 of Grünbaum-Shephard 1987 with A-numbers added and in some cases the name in the RCSR database]
%F Conjectures from _Colin Barker_, Apr 03 2020: (Start)
%F G.f.: (1 + 6*x + 22*x^2 + 6*x^3 + x^4) / ((1 - x)^2*(1 + x)^2).
%F a(n) = 2*a(n-2) - a(n-4) for n>4.
%F (End)
%Y Cf. A072154, A298039 (partial sums), A298036 (12-valent node), A298040 (tetravalent node).
%Y 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.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Jan 22 2018
%E Terms a(8)-a(54) added by _Tom Karzes_, Apr 01 2020
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