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 A157228 Number of primitive inequivalent inclined square sublattices of square lattice of index n. 8
 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,65 COMMENTS From Andrey Zabolotskiy, May 09 2018: (Start) Also, the number of partitions of n into 2 distinct coprime squares. All such sublattices (including non-primitive ones) are counted in A025441. The primitive sublattices that have the same symmetries (including the orientation of the mirrors) as the parent lattice are not counted here; they are counted in A019590, and all such sublattices (including non-primitive ones) are counted in A053866. For n > 2, equals A193138. (End) 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) = (A000089(n) - A019590(n)) / 2. - Andrey Zabolotskiy, May 09 2018 a(n) = 1 if n>2 is in A224450, a(n) = 2 if n is in A224770, a(n) is a higher power of 2 if n is in A281877 (first time reaches 8 at n = 32045). - Andrey Zabolotskiy, Sep 30 2018 CROSSREFS Cf. A193138, A145393 (all sublattices of the square lattice), A025441, A019590, A053866, A157226, A157230, A157231, A000089, A304182, A224450, A224770, A281877. Sequence in context: A014082 A322583 A102354 * A193138 A255320 A256574 Adjacent sequences:  A157225 A157226 A157227 * A157229 A157230 A157231 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 25 2009 EXTENSIONS New name and more terms from Andrey Zabolotskiy, May 09 2018 STATUS approved

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Last modified October 21 16:25 EDT 2019. Contains 328302 sequences. (Running on oeis4.)