%I #18 Mar 19 2021 08:48:08

%S 0,0,0,0,0,1,0,0,1,2,1,2,1,3,2,2,2,5,2,4,3,5,3,4,4,6,5,6,4,10,4,6,6,8,

%T 6,10,5,9,7,8,6,14,6,10,10,11,7,12,8,14,10,12,8,17,10,12,11,14,9,20,9,

%U 15,14,14,12,22,10,16,14,22,11,20,11,18,18,18

%N Number of primitive inequivalent oblique sublattices of hexagonal (triangular) lattice of index n (equivalence and symmetry of sublattices are determined using only parent lattice symmetries).

%H John S. Rutherford, <a href="http://dx.doi.org/10.1107/S010876730804333X">Sublattice enumeration. IV. Equivalence classes of plane sublattices by parent Patterson symmetry and colour lattice group type</a>, Acta Cryst. (2009). A65, 156-163. [See Table 5.]

%F a(n) = A003050(n) - (A000086(n)-A154272(n))/2 - A060594(n). - _Andrey Zabolotskiy_, Mar 19 2021

%Y Cf. A003051 (all sublattices), A003050 (all primitive sublattices), A154272 (primitive sublattices fully inheriting the parent lattice symmetry, inlcuding the orientation of the mirrors), A000086 (primitive rotation-symmetric sublattices, counting mirror images as distinct), A060594 (primitive mirror-symmetric sublattices), A145377 (all sublattices inheriting the parent lattice symmetry), A304182.

%K nonn

%O 1,10

%A _N. J. A. Sloane_, Feb 25 2009

%E New name and a(1)=0 prepended by _Andrey Zabolotskiy_, May 09 2018

%E Terms a(31) and beyond from _Andrey Zabolotskiy_, Mar 19 2021