A173715 Number of minimally rigid n x n adjacency matrices of sphere packings in R^3.

1, 1, 1, 1, 1, 4, 29, 438, 13828, 750352

Offset

1,6

Comments

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.

Links

Table of n, a(n) for n=1..10.

Natalie Arkus, Vinothan N. Manoharan, Michael P. Brenner. Deriving Finite Sphere Packings, Nov 24, 2010.

Crossrefs

Cf. A000088, A006125, A174423, A174424.

Sequence in context: A162287 A324227 A277357 * A230326 A272869 A166168

Adjacent sequences: A173712 A173713 A173714 * A173716 A173717 A173718

Keyword

nonn,hard

Author

Jonathan Vos Post, Nov 25 2010

Status

approved