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 A300812 Irregular triangle T(n,c) read by rows: the number of clusters of n spheres centered on f.c.c. lattice sites with c contacts. 1
 1, 0, 1, 0, 0, 3, 1, 0, 0, 0, 13, 4, 2, 1, 0, 0, 0, 0, 75, 35, 16, 3, 2, 0, 0, 0, 0, 0, 557, 384, 184, 54, 24, 5, 2, 1, 0, 0, 0, 0, 0, 0, 4808, 4230, 2354, 834, 355, 104, 37, 9, 2, 1, 0, 0, 0, 0, 0, 0, 0, 44334, 47328, 30517, 13081, 5716, 2083, 749, 253, 70, 20, 4, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Each of the n spheres is centered at a different vertex of the face-centered-cubic lattice. "Clusters of spheres" means that the (simple, undirected) graph, which has edges for each "bond" where two spheres touch, is connected. The number of contacts equals the number of edges in the graph. T(n,c) counts "free" clusters, which means that clusters are considered distinct if they cannot be mapped onto each other by one of the 48 symmetries of the octahedral group plus shifts along the directions of the face centers. Since there are 12 nearest neighbors in the f.c.c. lattice, the degree of each vertex in the contact graph is in the interval [1,12]. T(n,c) =0 for c

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Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)