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%I #12 Jan 08 2013 05:56:27
%S 1,1,1,1,1,4,29,438,13828,750352
%N Number of minimally rigid n x n adjacency matrices of sphere packings in R^3.
%C 3rd column of Table 1. The Growth of Adjacency Matrices with n, p.6, of Arkus. 2nd column is A000088 (number of equivalence classes of sign patterns of totally nonzero symmetric n X n matrices). 1st column might be A006125(n) = 2^(n(n-1)/2). We focus on enumerating only minimally rigid sphere packings; which we define as packings with >= 3 contacts per particle and >= 3n - 6 total contacts. Minimal rigidity is necessary, but not sufficient, for a structure to be rigid. Due to the large number of packings that must be evaluated, this analytical method is implemented computationally, and near n = 10 we reach the method's computational limitations.
%H Natalie Arkus, Vinothan N. Manoharan, Michael P. Brenner. <a href="http://arxiv.org/abs/1011.5412"> Deriving Finite Sphere Packings</a>, Nov 24, 2010.
%Y Cf. A000088, A006125, A174423, A174424.
%K nonn,hard
%O 1,6
%A _Jonathan Vos Post_, Nov 25 2010
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