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

1,4

Links

Table of n, a(n) for n=1..70.

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.]

Formula

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

Crossrefs

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

Sequence in context: A033097 A036845 A094269 * A054536 A293664 A001316

Adjacent sequences: A157224 A157225 A157226 * A157228 A157229 A157230

Keyword

nonn

Author

N. J. A. Sloane, Feb 25 2009

Extensions

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

Status

approved