A393906 Equivalence classes of clusters of n connected lozenges in the triangular grid.

1, 1, 3, 14, 77, 475, 3188, 22004, 156230, 1126536, 8226592, 60653744

Offset

0,3

Comments

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...)

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.

Links

Table of n, a(n) for n=0..11.

R. J. Mathar, Illustrations

Crossrefs

Cf. A056845.

Sequence in context: A369477 A394126 A394138 * A052186 A330518 A228656

Adjacent sequences: A393903 A393904 A393905 * A393907 A393908 A393909

Keyword

nonn,more

Author

R. J. Mathar, Mar 02 2026

Extensions

a(8)-a(11) from Pontus von Brömssen, Mar 03 2026

Status

approved