[Community Puzzle] Unfolding Paper missing Testcases

Puzzles
#1

In the new Community Puzzle Unfolding Paper are 3 testcases missing.
You can break the problem down to a number sequence and notice, that startpieces are missing.
For a complete puzzle you need startpieces where

  1. a startpiece pattern touches only left and right
  2. a startpiece pattern touches only left and right and the top
  3. a startpiece pattern touches only left and right and bottom

These pieces can’t be created by other startpieces (believe me, i can proof!) and loop in each other.

if you unfold a pattern with case1 you get 2 times the pattern of case1
if you unfold a pattern with case2 you get 1 times the pattern of case1
if you unfold a pattern with case3 you get a pattern of case3 and a pattern of case2

Therefore a startpattern like

.....
.....
#####
..#..
..#..

would create full test coverage after unfolding it 3 times.

Sorry for my bad english and have a nice day,
Essigautomat