A binary partition of an integer m is a is a numerical partition of m , all of whose parts are powers of 2. This is sequence A000123 in Sloane's database of integer sequences.
Binary partitions satisfy the following recurrence relation.
To see that this recurrence relation is correct, classify the partitions according to whether 1 is a part or not. If 1 is a part, remove it, obtaining a partition counted by b n- 1 . This page maintained by Bullwinkle .