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A054384
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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.
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2
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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; internal format)
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OFFSET
| 0,4
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COMMENTS
| The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
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REFERENCES
| 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, (njas(AT)research.att.com), Feb 23 2009]
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LINKS
| 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
Index entries for sequences related to sublattices
Index entries for sequences related to A2 = hexagonal = triangular lattice
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CROSSREFS
| Cf. A003051, A054346.
Sequence in context: A141285 A157893 A199474 * A026400 A026409 A085238
Adjacent sequences: A054381 A054382 A054383 * A054385 A054386 A054387
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 08 2000
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