A157231 - OEIS

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A157231

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

6

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

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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