[seqfan] Rotationally and reflectionally incongruent patches of triangles

[Felix Fröhlich]

Dear sequence fans,

I have the following sequence:

a(n) = number of rotationally and reflectionally incongruent triangular
patches that can be built from black and white triangles.

Offset = 2, where n counts the length of one side of a large triangle in
terms of sides of small triangles.

a(2) = 2, because only two large triangles with side length 2 are possible
which remain incongruent under rotations and reflections.

a(3) is at least 17 (see illustration in attached PDF).

Is there an easy method to determine more terms of this sequence? I believe
the size of the terms will grow quickly and determining them "by hand"
might be infeasible for larger n.

Felix