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%I #36 Mar 07 2024 10:59:10
%S 1,3,7,12,17,23,28,33,37,42,47,51,56,61,65,70,75,79,84,89,93,98,103,
%T 107,112,117,121,126,131,135,140,145,149,154,159,163,168,173,177,182,
%U 187,191,196,201,205,210,215,219,224,229,233,238,243,247,252,257,261
%N Coordination sequence for Dual(3^3.4^2) tiling with respect to a trivalent node.
%C This tiling is also called the prismatic pentagonal tiling, or the cem-d net. It is one of the 11 Laves tilings.
%D B. Gruenbaum and G. C. Shephard, Tilings and Patterns, W. H. Freeman, New York, 1987. See p. 96.
%H Rémy Sigrist, <a href="/A298022/b298022.txt">Table of n, a(n) for n = 0..1000</a>
%H Chung, Ping Ngai, Miguel A. Fernandez, Yifei Li, Michael Mara, Frank Morgan, Isamar Rosa Plata, Niralee Shah, Luis Sordo Vieira, and Elena Wikner. <a href="http://dx.doi.org/10.1090/noti838">Isoperimetric Pentagonal Tilings</a>, Notices of the AMS 59, no. 5 (2012), pp. 632-640. See Fig. 1 (right).
%H Tom Karzes, <a href="/A250122/a250122.html">Tiling Coordination Sequences</a>
%H Frank Morgan, <a href="https://www.youtube.com/watch?v=PpUx0nnWfKQ">Optimal Pentagonal Tilings</a>, Video, May 2021 [Mentions this tiling
%H Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/layers/cem-d">The cem-d tiling (or net)</a>
%H Rémy Sigrist, <a href="/A298022/a298022.gp.txt">PARI program for A298022</a>
%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 N. J. A. Sloane, <a href="/A298022/a298022.png">Illustration of initial terms</a>
%F Conjectures from _Colin Barker_, Jan 22 2018: (Start)
%F 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)).
%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>5.
%F (End)
%o (PARI) See Links section.
%Y See A298023 for partial sums, A298024 for a tetravalent point.
%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 21 2018
%E More terms from _Rémy Sigrist_, Jan 21 2018
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