A182718 - OEIS

%I #8 Dec 01 2013 13:35:01

%S 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

%N 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.

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

%C 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.

%C I would like a table for this sequence!

%C I would like to see the graphic!

%e Triangle begins:

%e 1,

%e 2,

%e 3,

%e 4, 2,

%e 5, 3,

%e 6, 3, 4, 2,

%e 7, 4, 5, 3,

%e 8, 4, 5, 6, 3, 4, 2,

%e 9, 5, 6, 3, 7, 4, 5, 3,

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

%Y Column 1 gives A000027.

%K nonn,tabf

%O 1,2

%A _Omar E. Pol_, Jan 26 2011