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

Author

N. J. A. Sloane, Feb 25 2009

Keywords

• nonn

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.]

Crossrefs

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

Formula

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

Extensions

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