A157227 - OEIS

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A157227

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

2

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

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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