A182718 Largest part of the n-th row of the diagram of another version of the shell model of partitions in which each last section of partitions is represented by a tree.

1, 2, 3, 4, 2, 5, 3, 6, 3, 4, 2, 7, 4, 5, 3, 8, 4, 5, 6, 3, 4, 2, 9, 5, 6, 3, 7, 4, 5, 3

Offset

1,2

Comments

The same positive integers of the triangle of A141285 but here each row lists the terms in reverse order.

It appears that the version of the shell model of partitions which gives this sequence also shows a connection between the partition theory and the graph theory because the structure looks like a forest or grove in which each last section is a tree. In a three-dimensional version of the structure we can see that one of the views shows the branches of the trees of the even numbers tilted 45 degrees to the left and the branches of the trees of the odd numbers tilted 45 degrees to the right. Another view contains the "roots" of trees, the tables of both A182982 and A182983.

I would like a table for this sequence!

I would like to see the graphic!

Links

Table of n, a(n) for n=1..30.

Example

Triangle begins:
1,
2,
3,
4, 2,
5, 3,
6, 3, 4, 2,
7, 4, 5, 3,
8, 4, 5, 6, 3, 4, 2,
9, 5, 6, 3, 7, 4, 5, 3,

Crossrefs

Cf. A135010, A138121, A141285, A182742, A182743, A182982, A182983.

Column 1 gives A000027.

Sequence in context: A305893 A325980 A366122 * A212645 A364951 A364950

Adjacent sequences: A182715 A182716 A182717 * A182719 A182720 A182721

Keyword

nonn,tabf

Author

Omar E. Pol, Jan 26 2011

Status

approved