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Number of inequivalent sublattices of index n in hexagonal lattice (two sublattices are equivalent if one can be rotated or reflected to give the other).
(Formerly M0420)

+0
9

1, 1, 2, 3, 2, 3, 3, 5, 4, 4, 3, 8, 4, 5, 6, 9, 4, 8, 5, 10, 8, 7, 5, 15, 7, 8, 9, 13, 6, 14, 7, 15, 10, 10, 10, 20, 8, 11, 12, 20, 8, 18, 9, 17, 16, 13, 9, 28, 12, 17, 14, 20, 10, 22, 14, 25, 16, 16, 11, 34, 12, 17, 21, 27, 16, 26, 13, 24, 18, 26, 13, 40, 14 (list; graph; listen)

	OFFSET	`1,3`
	COMMENT	`The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.`
	REFERENCES	`A. Altshuler, Construction and enumeration of regular maps on the torus, Discrete Math. 4 (1973), 201-217.`
	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`
	FORMULA	`a(n) = Sum_{ m^2 \| n } A003050(n/m^2).`
	CROSSREFS	`Cf. A003050, A054384, A001615, A006984, A054345.` `Sequence in context: A030582 A036762 A032154 this_sequence A097352 A076050 A130799` `Adjacent sequences: A003048 A003049 A003050 this_sequence A003052 A003053 A003054`
	KEYWORD	`nonn,nice,easy`
	AUTHOR	`njas`

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.

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