5, 4+1, 3+2, 3+1+1, 2+2+1, 2+1+1+1 and 1+1+1+1+1.
The number of ways that a given number may be broken up is far from a simple matter, and has been the object of study since the mid-seventeen hundreds.Polyominoes can be partitioned into smaller ones. Following tables show partitions for n <= 5. Were done by hand and corrected by Wei-Hwa Huang. A sequence of partitions for polyominoes of order 1, 2, 3, 4, 5... is:
1, 2, 6, 31, 156...
Partitions for other polyforms would give other sequences.The monomino partition:
The 2 dominoes partitions:
The 6 trominoes partitions:
The 31 tetrominoes partitions:
The 156 pentominoes partitions:
Jorge Mireles. Aug 19, 2006
