draft

3: (2, 1) 4: (3, 1) 5: (4, 1), (3, 2) 6: (5, 1), (3, 2, 1), (4, 2) 7: (6, 1), (5, 2), (4, 3), (4, 2, 1) 8: (7, 1), (6, 2), (5, 3), (5, 2, 1), (4, 3, 1) 9: (5, 4), (4, 3, 2) 10: (5, 4, 1), (5, 3, 2), (4, 3, 2, 1) 11: (6, 5), (6, 4, 1), (6, 3, 2), ()

n: (n-1, 1), (n-2, 2)... there are (n-1)//2 of these pairs