login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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