A157224 Number of primitive inequivalent (up to Pi/2 rotation) nonsquare sublattices of square lattice of index n.

0, 1, 2, 3, 2, 6, 4, 6, 6, 8, 6, 12, 6, 12, 12, 12, 8, 18, 10, 18, 16, 18, 12, 24, 14, 20, 18, 24, 14, 36, 16, 24, 24, 26, 24, 36, 18, 30, 28, 36, 20, 48, 22, 36, 36, 36, 24, 48, 28, 44, 36, 42, 26, 54, 36, 48, 40, 44, 30, 72, 30, 48, 48, 48, 40, 72, 34, 54

Offset

1,3

Links

Table of n, a(n) for n=1..68.

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) - A000089(n))/2. - Andrey Zabolotskiy, May 09 2018

Crossrefs

Cf. A000089 (primitive square sublattices), A002654 (all square sublattices), A145392 (all sublattices), A001615, A304182.

Sequence in context: A197289 A161888 A347859 * A097914 A286633 A286586

Adjacent sequences: A157221 A157222 A157223 * A157225 A157226 A157227

Keyword

nonn

Author

N. J. A. Sloane, Feb 25 2009

Extensions

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

Status

approved