cp's OEIS Frontend

It would be nice to have a definition of "polypon"! - N. J. A. Sloane, May 09 2007

By looking at the Clarke pictures, I guess that the unit element is a triangle with internal angles of 120 degrees and two of 30 degrees. The polypons are connected, nonoverlapping assemblies of these, where connectivity is defined via common sides; a common point is not enough. Only non-congruential assemblies are counted, those which cannot be mapped onto each other by rotations, translations or mirrors along a line or point. However, the polypons are not all of these, because some of the free-form assemblies of this kind would need placement of the unit that violates the format by the grid. (The first case where this happens is with assemblies of 3 units: the picture shows 2 examples with assemblies of 3 units, but I can imagine at least 1 more where the unit would need to hide/cover one of the grid's edges.) - R. J. Mathar, Dec 10 2007

A polypon is a polyform made up of 30-30-120 triangles from the [3.12^2] Laves tiling, joined along their edges. Because that tiling contains hexagons formed as a union of six triangles, with the division of the hexagon having less symmetry than the hexagon on its own, some polypons can be divided into their constituent triangles in more than one way, and whether the division is significant affects the values of a(n) when n >= 18 is a multiple of 6. For the present sequence, the division into triangles is considered significant. - Joseph Myers, Oct 02 2011