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%I #13 Mar 07 2026 04:49:54
%S 1,1,3,14,77,475,3188,22004,156230,1126536,8226592,60653744
%N Equivalence classes of clusters of n connected lozenges in the triangular grid.
%C Lozenges are connected in the sense that they share edges, but must not overlap. This is a variant of A056845: Here equivalence considers clusters applying the reduced symmetry point group of C_6, which means clusters that can be mapped by using reflections are distinct (unless they can be mapped by pure rotations...)
%C a(n) grows roughly twice as fast as A056845(n) because at large n the clusters which are mirror-symmetric are only a small set of all clusters.
%H R. J. Mathar, <a href="/A056845/a056845.pdf">Illustrations</a>
%Y Cf. A056845.
%K nonn,more
%O 0,3
%A _R. J. Mathar_, Mar 02 2026
%E a(8)-a(11) from _Pontus von Brömssen_, Mar 03 2026