Covering Free Polyominos

free polyomino - an arrangement of N cells, unique under rotation, translation, and flips (A000105).
path coverable - this means the polyomino can be covered by a path; the polyomino can be completely covered by a self-avoiding walk (A252653).
coil coverable - the polyomino can be covered by a path which obeys mortal coil rules - it is a complete self-avoiding walk, but has the additional restraint of only being able to turn once it can no longer move in the same direction.

	count	path-coverable	coil-coverable
Polyominos of 1 cell	1	1	1
Polyominos of 2 cells	1	1	1
Polyominos of 3 cells	2	2	2
Polyominos of 4 cells	5	4	4
Polyominos of 5 cells	12	8	8
Polyominos of 6 cells	35	18	17
Polyominos of 7 cells	108	46	44
Polyominos of 8 cells	369	115	102
Polyominos of 9 cells	1285	300	261
Polyominos of 10 cells	4655	781	635
Polyominos of 11 cells	17073	2097	1632
Polyominos of 12 cells	63600	5541	4045

page by Ernest French. akasatanahamayarawan@gmail.com