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 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) 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

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