%I #36 Jun 08 2024 20:17:41

%S 1,4,20,24,40,40,60,56,80,72,100,88,120,104,140,120,160,136,180,152,

%T 200,168,220,184,240,200,260,216,280,232,300,248,320,264,340,280,360,

%U 296,380,312,400,328,420,344,440,360,460,376,480,392,500,408,520,424,540

%N Coordination sequence of Dual(4.6.12) tiling with respect to a tetravalent node.

%H Harvey P. Dale, <a href="/A298040/b298040.txt">Table of n, a(n) for n = 0..1000</a>

%H Tom Karzes, <a href="/A250122/a250122.html">Tiling Coordination Sequences</a>

%H N. J. A. Sloane, <a href="/A298040/a298040.png">Illustration of initial terms</a> (shows one 90-degree quadrant 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]

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).

%F Conjecture: For n>0, a(n)=10n if n even, otherwise 8n.

%F Conjectures from _Colin Barker_, Apr 01 2020: (Start)

%F G.f.: (1 + 4*x + 18*x^2 + 16*x^3 + x^4 - 4*x^5) / ((1 - x)^2*(1 + x)^2).

%F a(n) = (9 + (-1)^n)*n for n>1.

%F a(n) = 2*a(n-2) - a(n-4) for n>5.

%F (End)

%t LinearRecurrence[{0,2,0,-1},{1,4,20,24,40,40},60] (* _Harvey P. Dale_, Apr 06 2022 *)

%Y Cf. A072154, A298041 (partial sums), A298036 (12-valent node), A298038 (hexavalent 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,easy

%O 0,2

%A _N. J. A. Sloane_, Jan 22 2018

%E Terms a(8)-a(54) added by _Tom Karzes_, Apr 01 2020