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

1,2

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).

Links

Table of n, a(n) for n=1..42.

Example

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.

Sequence in context: A255542 A117500 A297626 * A175245 A167413 A373198

Adjacent sequences: A206438 A206439 A206440 * A206442 A206443 A206444

Keyword

nonn,tabf,more

Author

Omar E. Pol, Feb 13 2012

Status

approved