A206441 Triangle read by rows. T(n,k) = number of distinct parts in the k-th region of the last section of the set of partitions of n.

1, 2, 2, 1, 3, 1, 3, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 3, 1, 1, 5, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 1, 4, 1, 2, 1, 1, 6

Offset: 1

Author

Omar E. Pol, Feb 13 2012

Keywords

• nonn
• tabf
• more

Comments

a(n) is also the number of distinct parts in the n-th region of the shell model of partitions (see A135010 and A206437).

Examples

			The first region in the last section of the set of partitions of 6 looks like this:
.        **
There is only one part, so T(6,1) = 1.
The second region in the last section of the set of partitions of 6 looks like this:
.        ****
.          **
There are two distinct parts, so T(6,2) = 2.
The third region in the last section of the set of partitions of 6 looks like this:
.        ***
There is only one part, so T(6,3) = 1.
The 4th region in the last section of the set of partitions of 6 looks like this:
.        ******
.           ***
.            **
.            **
.             *
.             *
.             *
.             *
.             *
.             *
.             *
There are four distinct parts, so T(6,4) = 4.
Written as a triangle:
1;
2;
2;
1, 3;
1, 3;
1, 2, 1, 4;
1, 2, 1, 4;
1, 2, 1, 3, 1, 1, 5;
1, 2, 1, 3, 1, 2, 1, 5;
1, 2, 1, 3, 1, 1, 4, 1, 2, 1, 1, 6;
		

Crossrefs

Row n has length A187219(n).

Cf. A135010, A138121, A141285, A186412, A193870, A194436, A194437, A194438, A194439, A194446, A194447.