A304183 Number of primitive inequivalent oblique sublattices of rectangular lattice of index n.

0, 0, 1, 1, 2, 3, 3, 4, 5, 6, 5, 8, 6, 9, 10, 10, 8, 15, 9, 14, 14, 15, 11, 20, 14, 18, 17, 20, 14, 30, 15, 22, 22, 24, 22, 32, 18, 27, 26, 32, 20, 42, 21, 32, 34, 33, 23, 44, 27, 42, 34, 38, 26, 51, 34, 44, 38, 42, 29, 64, 30, 45, 46, 46, 40, 66, 33, 50, 46

Offset: 1

Author

Andrey Zabolotskiy, May 07 2018

Keywords

• nonn

Links

• 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. Contains errors for n = 24 and 28.]

Crossrefs

Cf. A304182 (primitive mirror-symmetric sublattices), A069734 (all sublattices), A001615 (primitive sublattices of oblique lattice).

Formula

a(n) = (A001615(n) - A304182(n))/2.