A157231 Number of primitive inequivalent oblique sublattices of square lattice of index n (equivalence and symmetry of sublattices are determined using parent lattice symmetries).

0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 2, 4, 4, 4, 3, 7, 4, 6, 6, 7, 5, 8, 6, 8, 8, 9, 6, 14, 7, 10, 10, 11, 10, 15, 8, 13, 12, 14, 9, 20, 10, 15, 16, 16, 11, 20, 13, 20, 16, 18, 12, 25, 16, 20, 18, 20, 14, 30, 14, 22, 22, 22, 18, 32, 16, 24, 22, 32, 17, 32, 17

Offset

1,9

Links

Andrey Zabolotskiy, Table of n, a(n) for n = 1..5000

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 5.]

Formula

a(n) = (A001615(n) - A019590(n) - 2 * (A157228(n) + A157226(n) + A157230(n))) / 4. - Andrey Zabolotskiy, May 09 2018

Crossrefs

Cf. A145393 (all sublattices of the square lattice), A019590, A157228, A157226, A157230, A001615, A304182.

Sequence in context: A286545 A046798 A329434 * A332888 A258596 A273784

Adjacent sequences: A157228 A157229 A157230 * A157232 A157233 A157234

Keyword

nonn

Author

N. J. A. Sloane, Feb 25 2009

Extensions

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

Status

approved