A122675 Number of "fragments" with n nodes generated from the simple cubic lattice.

1, 1, 2, 9, 29, 165, 962, 6423

Offset

1,3

Comments

The "fragments" are generated as follows. For each of the polycubes with n cells, counted by A000162(n) or b(n) = A038119(n), consider two possible ways to inscribe a tetrahedron into each cell so that the tetrahedra in any two neighboring cells share an edge. The centers of the cells correspond to cations in the antifluorite structure, while the vertices of the tetrahedra correspond to anions. a(n) is the number of resulting tetrahedral clusters; enantiomorphic pairs are counted as one. Thus b(n) <= a(n) <= 2*b(n). - Andrey Zabolotskiy, Mar 04 2023

Links

Table of n, a(n) for n=1..8.

J. R. Long and R. H. Holm, Enumeration and Structural Classification of Clusters Derived from Parent Solids: Metal-Chalcogenide Clusters Composed of Edge-Sharing Tetrahedra, J. Amer. Chem. Soc., 116 (1994), 9987-10002.

Wikipedia, Fluorite structure

Crossrefs

Cf. A000162, A038119, A122673, A122674.

Sequence in context: A150903 A151306 A150904 * A042357 A079783 A182975

Adjacent sequences: A122672 A122673 A122674 * A122676 A122677 A122678

Keyword

nonn,more

Author

N. J. A. Sloane, Sep 23 2006

Status

approved