Search: id:A054384
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%I A054384
%S A054384 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,
%T A054384 10,24,11,21,16,18,14,31,13,19,18,30,14,28,15,28,26,24,16,42,17,31,
%U A054384 24,31,18,40,24,35,26,30,20,56,21,31,31,43,26,48,23,42,32,42,24,65
%N 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.
%C A054384 The hexagonal lattice is the familiar 2-dimensional lattice in which 
               each point has 6 neighbors. This is sometimes called the triangular 
               lattice.
%D A054384 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]
%H A054384 M. Bernstein, N. J. A. Sloane and P. E. Wright, On Sublattices of the 
               Hexagonal Lattice, Discrete Math. 170 (1997) 29-39 (<a href="http:/
               /www.research.att.com/~njas/doc/paul.txt">Abstract</a>, <a href="http:/
               /www.research.att.com/~njas/doc/paul.pdf">pdf</a>, <a href="http:/
               /www.research.att.com/~njas/doc/paul.ps">ps</a>).
%H A054384 G. Nebe and N. J. A. Sloane, <a href="http://www.research.att.com/~njas/
               lattices/A2.html">Home page for hexagonal (or triangular) lattice 
               A2</a>
%H A054384 <a href="Sindx_Su.html#sublatts">Index entries for sequences related 
               to sublattices</a>
%H A054384 <a href="Sindx_Aa.html#A2">Index entries for sequences related to A2 
               = hexagonal = triangular lattice</a>
%Y A054384 Cf. A003051, A054346.
%Y A054384 Sequence in context: A159081 A141285 A157893 this_sequence A026400 A026409 
               A085238
%Y A054384 Adjacent sequences: A054381 A054382 A054383 this_sequence A054385 A054386 
               A054387
%K A054384 nonn,nice,easy
%O A054384 0,4
%A A054384 N. J. A. Sloane (njas(AT)research.att.com), May 08 2000

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