1,3

The next level gets created from each node by adding one or two more nodes. If a single node is added, its value is one more than the value of its parent. If two nodes are added, the first is equal in value to the parent and the value of the second is one more than the value of the parent.

Sequence A036043 counts the parts of numeric partitions and contains the same values on each row as the current sequence. When a node generates two branches the first branch can be mapped to cyclic partitions; all other branches map to matching partitions.

The values at level three are 1 2 & 3

The 1 generates 1 & 2; the 2 generates 2 & 3; the 3 only generates 4.

The array begins

1

1 2

1 2 3

1 2 2 3 4

1 2 2 3 3 4 5

1 2 2 3 2 3 4 3 4 5 6

Cf. A000041 A060850 A128629.

Cf. A006128 (row sums), A036043.

Adjacent sequences: A128625 A128626 A128627 this_sequence A128629 A128630 A128631

Sequence in context: A094917 A082691 A036043 this_sequence A098053 A128117 A023115

nonn,tabf

Alford Arnold (Alford1940(AT)aol.com), Mar 27 2007, Aug 01 2007