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A111189 Number of polyanygons (or Pollyannagons) with score n, with all symmetries removed. 0
1, 2, 3, 9, 20, 75, 255 (list; graph; refs; listen; history; text; internal format)



Polyanygons are like polyominoes, but they are built by gluing together arbitrary regular polygons of side 1.

The score for a polyanygon is the total of its components' scores. Triangle = 1, square = 2, N-gon = N-2.

Holes are allowed. Nonzero area overlap of polygons is forbidden. Glued edges must line up vertex to vertex. Non-glued edges may occasionally have a slide offset and vertices may touch edges internally or contact other vertices. Higher scoring polyanygons can have partially offset edges, so the perimeter is not always an integer.

A regular hexagon is regarded as different from the same shape made out of six triangles and a dodecagon is different from a hexagon plus an alternating triangle/square fringe. Two polyanygons made of the same regular polygons in the same relative positions and orientations, but differing in order of assembly or which edges are glued, are considered the same.


Table of n, a(n) for n=1..7.


The 3 polyanygons of score 3 are the triamond (three equilateral triangles), a square stuck to a triangle (a house) and the regular pentagon.


Sequence in context: A245123 A097075 A036673 * A001004 A015951 A244666

Adjacent sequences:  A111186 A111187 A111188 * A111190 A111191 A111192




Richard C. Schroeppel, Oct 23 2005



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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)