
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
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OFFSET

0,4


COMMENTS

The hexagonal lattice is the familiar 2dimensional 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) 2939 (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, 156163 [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

