A157227 Number of primitive inequivalent (up to Pi/3 rotation) non-hexagonal sublattices of hexagonal (triangular) lattice of index n.

0, 1, 1, 2, 2, 4, 2, 4, 4, 6, 4, 8, 4, 8, 8, 8, 6, 12, 6, 12, 10, 12, 8, 16, 10, 14, 12, 16, 10, 24, 10, 16, 16, 18, 16, 24, 12, 20, 18, 24, 14, 32, 14, 24, 24, 24, 16, 32, 18, 30, 24, 28, 18, 36, 24, 32, 26, 30, 20, 48, 20, 32, 32, 32, 28, 48, 22, 36, 32, 48

Offset: 1

Author

N. J. A. Sloane, Feb 25 2009

Keywords

• nonn

Links

• John S. Rutherford, Sublattice enumeration. IV. Equivalence classes of plane sublattices by parent Patterson symmetry and colour lattice group type, Acta Cryst. (2009). A65, 156-163. [See Table 4.]

Crossrefs

Cf. A000086 (primitive hexagonal sublattices), A002324 (all hexagonal sublattices), A145394 (all sublattices), A001615, A304182.

Formula

a(n) = (A001615(n) - A000086(n))/3. - Andrey Zabolotskiy, May 09 2018

Extensions

New name and more terms from Andrey Zabolotskiy, May 09 2018