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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054345 Number of inequivalent sublattices of index n in square lattice, where two lattices are considered equivalent if one can be rotated to give the other. 8
1, 1, 2, 2, 4, 3, 6, 4, 8, 7, 8, 6, 14, 7, 12, 10, 16, 9, 20, 10, 18, 16, 18, 12, 30, 13, 20, 20, 28, 15, 30, 16, 32, 24, 26, 20, 46, 19, 30, 26, 38, 21, 48, 22, 42, 33, 36, 24, 62, 29, 38, 34, 46, 27, 60, 30, 60, 40, 44, 30, 70, 31, 48, 52, 64, 33, 72, 34, 60, 48, 60 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

If reflections are allowed, we get A054346. If only rotations that preserve the parent square lattice are allowed, we get A145392. The analog for hexagonal lattice is A054384.

LINKS

Andrey Zabolotskiy, Table of n, a(n) for n = 0..1000

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. - From N. J. A. Sloane, Feb 23 2009

Andrey Zabolotskiy, Sublattices of the square lattice (illustrations for n = 1..6, 15, 25)

Index entries for sequences related to sublattices

Index entries for sequences related to square lattice

EXAMPLE

For n = 1, 2, 3, 4 the sublattices are generated by the rows of:

[1 0] [2 0] [2 0] [3 0] [3 0] [4 0] [4 0] [2 0] [2 0]

[0 1] [0 1] [1 1] [0 1] [1 1] [0 1] [1 1] [0 2] [1 2].

CROSSREFS

Cf. A003051, A001615, A054346, A054384, A145392.

Sequence in context: A060766 A321015 A029578 * A304214 A060367 A267451

Adjacent sequences:  A054342 A054343 A054344 * A054346 A054347 A054348

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, May 06 2000

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 17 18:58 EDT 2019. Contains 328127 sequences. (Running on oeis4.)