

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
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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, 156163.  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



