login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054384 Number of inequivalent sublattices of index n in hexagonal lattice, where two lattices are considered equivalent if one can be rotated to give the other. 5
1, 1, 1, 2, 3, 2, 4, 3, 5, 5, 6, 4, 10, 5, 7, 8, 11, 6, 13, 7, 14, 10, 12, 8, 20, 11, 13, 14, 17, 10, 24, 11, 21, 16, 18, 14, 31, 13, 19, 18, 30, 14, 28, 15, 28, 26, 24, 16, 42, 17, 31, 24, 31, 18, 40, 24, 35, 26, 30, 20, 56, 21, 31, 31, 43, 26, 48, 23, 42, 32, 42, 24, 65 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

If reflections are allowed, we get A300651. If only rotations that preserve the parent hexagonal lattice are allowed, we get A145394. The analog for square lattice is A054345. - Andrey Zabolotskiy, Mar 10 2018

LINKS

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

M. Bernstein, N. J. A. Sloane and P. E. Wright, On Sublattices of the Hexagonal Lattice, Discrete Math. 170 (1997) 29-39 (Abstract, pdf, ps).

G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

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

Andrey Zabolotskiy, Sublattices of the hexagonal lattice (illustrations for n = 1..7, 14)

Index entries for sequences related to sublattices

Index entries for sequences related to A2 = hexagonal = triangular lattice

CROSSREFS

Cf. A003051, A054345, A054346, A145394, A300651.

Sequence in context: A283368 A199474 A246694 * A026400 A026409 A336215

Adjacent sequences:  A054381 A054382 A054383 * A054385 A054386 A054387

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane, May 08 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 June 17 17:46 EDT 2021. Contains 345085 sequences. (Running on oeis4.)