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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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 A259176

Adjacent sequences:  A206438 A206439 A206440 * A206442 A206443 A206444

KEYWORD

nonn,tabf,more

AUTHOR

Omar E. Pol, Feb 13 2012

STATUS

approved

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Last modified April 19 20:40 EDT 2019. Contains 322291 sequences. (Running on oeis4.)