This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A157235 #18 Mar 19 2021 08:48:08 %S A157235 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 A157235 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 A157235 15,14,14,12,22,10,16,14,22,11,20,11,18,18,18 %N A157235 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 A157235 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 A157235 a(n) = A003050(n) - (A000086(n)-A154272(n))/2 - A060594(n). - _Andrey Zabolotskiy_, Mar 19 2021 %Y A157235 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 A157235 nonn %O A157235 1,10 %A A157235 _N. J. A. Sloane_, Feb 25 2009 %E A157235 New name and a(1)=0 prepended by _Andrey Zabolotskiy_, May 09 2018 %E A157235 Terms a(31) and beyond from _Andrey Zabolotskiy_, Mar 19 2021