From Andrey Zabolotskiy, Nov 09 2018: (Start)
There are no 2step polygons (conventionally).
For n=2, the only 4step polygon is a 1 X 1 square having span 1, so a(2)=1.
For n=3, the only 6step polygon is a 2 X 1 domino which can be rotated 2 ways having spans 2 and 1, so a(3) = 2+1 = 3.
For n=4, there are the following 8step polygons:
a 3 X 1 stick which can be rotated 2 ways having spans 3 and 1;
an Ltromino which can be rotated 4 ways, all having span 2;
a 2 X 2 square, having span 2.
So a(4) = 3 + 1 + 4*2 + 2 = 14.
For n=5, there are the following 10step polygons:
a 4 X 1 stick which can be rotated 2 ways having spans 4 and 1;
an Ltetromino which can be rotated 2 ways with span 2 and 2 more ways with span 3, plus reflections;
a Ttetromino which can be rotated 2 ways with span 2 and 2 more ways with span 3;
an Stetromino which can be rotated 2 ways having spans 3 and 2, plus reflections;
a 3 X 2 rectangle which can be rotated 2 ways having spans 3 and 2;
a 3 X 2 rectangle without one of its angular squares having same counts as Ltetromino.
So a(5) = 4 + 1 + 2 * 2*2*(2+3) + 2*(2+3) + 2*(3+2) + 3 + 2 = 70.
(End)
