%I #39 Jun 21 2018 10:15:36
%S 1,5,8,8,11,17,25,27,24,30,38,46,47,44,46,50,64,68,65,66,70,80,80,83,
%T 87,91,100,100,99,99,109,121,121,119,119,125,133,139,140,140,145,153,
%U 155,152,158,166,174,175,172,174,178,192,196,193,194,198,208,208,211
%N Coordination sequence of point of type 3.3.4.3.4 in 4-uniform tiling {3.3.4.3.4; 3.3.4.12; 3.3.12.4; 3.4.3.12}.
%C This tiling appears as an example in Connelly et al. (2014), Fig. 6 (the heavy black lines in the figures here are an artifact from that figure).
%C For the definition of k-uniform tiling see Section 2.2 of Chapter 2 of Grünbaum and Shephard (1987).
%D Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987.
%H Joseph Myers, <a href="/A250123/b250123.txt">Table of n, a(n) for n = 0..1000</a>
%H Robert Connelly, Jeffrey D. Shen, Alexander D. Smith, <a href="http://arxiv.org/abs/1301.0664">Ball Packings with Periodic Constraints</a>, arXiv:1301.0664 [math.MG], 2013.
%H Robert Connelly, Jeffrey D. Shen, Alexander D. Smith, <a href="http://dx.doi.org/10.1007/s00454-014-9636-z">Ball Packings with Periodic Constraints</a>, Discrete Comput. Geom. 52 (2014), no. 4, 754--779. MR3279548.
%H Brian Galebach, <a href="http://probabilitysports.com/tilings.html?u=0&n=4&t=132">Tiling 132</a> (in list of 4-uniform tilings).
%H Brian Galebach, <a href="/A250120/a250120.html">k-uniform tilings (k <= 6) and their A-numbers</a>
%H N. J. A. Sloane, <a href="/A250123/a250123_3.png">A portion of the 3-uniform tiling {3.3.4.3.4; 3.3.4.12; 3.3.12.4; 3.4.3.12}</a>. The four black dots labeled P,Q,R,S show the four types of point. The present sequence is for a point of type P.
%H N. J. A. Sloane, <a href="/A250123/a250123_1.png">Shows layers a(0)-a(6)</a>
%F Empirical g.f.: -(x+1)*(x^15 +3*x^14 -4*x^11 -6*x^10 -7*x^9 -4*x^8 -7*x^7 -11*x^6 -9*x^5 -7*x^4 -4*x^3 -4*x^2 -4*x -1) / ((x -1)^2*(x^4 +x^3 +x^2 +x +1)*(x^6 +x^5 +x^4 +x^3 +x^2 +x +1)). - _Colin Barker_, Dec 02 2014
%Y Cf. A250124, A250125, A250126.
%Y List of coordination sequences for uniform planar nets: A008458 (the planar net 3.3.3.3.3.3), A008486 (6^3), A008574 (4.4.4.4 and 3.4.6.4), A008576 (4.8.8), A008579 (3.6.3.6), A008706(3.3.3.4.4), A072154 (4.6.12), A219529 (3.3.4.3.4), A250120 (3.3.3.3.6), A250122 (3.12.12).
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Nov 29 2014
%E Galebach link from _Joseph Myers_, Nov 30 2014
%E Extended by _Joseph Myers_, Dec 02 2014