A182813 Triangle read by rows in which row n lists the parts of the largest subshell of all partitions of 2n+1 that do not contain 1 as a part.

3, 5, 2, 7, 4, 3, 2, 2, 9, 5, 4, 6, 3, 3, 3, 3, 2, 2, 2, 2, 11, 6, 5, 7, 4, 8, 3, 4, 4, 3, 5, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 13, 7, 6, 8, 5, 9, 4, 5, 4, 4, 10, 3, 5, 5, 3, 6, 4, 3, 7, 3, 3, 4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset

1,1

Comments

In the shell model of partitions the head of the last section of the set of partitions of 2n+1 contains n subshells.

The first n rows of this triangle represent these subsells.

This sequence contains the same elements of A182743 but in distinct order.

See A135010 and A138121 for more information.

Links

Table of n, a(n) for n=1..80.

Example

For n=1 the unique partition of 2n+1=3 that does not contains 1 as part is 3, so row 1 has an element = 3.
For n=2 there are 2 partitions of 2n+1=5 that do not contain 1 as part:
5 ............ or ....... 5 . . . .
3 + 2 ........ or .......(3). . 2 .
These partitions contain (3), the row n-1 of triangle, so
the parts of the largest subshell are 5, 2.
For n=3 there are 4 partitions of 2n+1=7 that do not contain 1 as part:
7 ............ or ....... 7 . . . . . .
4 + 3 ........ or ....... 4 . . . 3 . .
5 + 2 ........ or .......(5). . . . 2 .
3 + 2 + 2 .... or .......(3). .(2). 2 .
These partitions contain (5) and (3),(2), the parts of the rows < n of triangle, so the parts of the largest subshell are 7, 4, 3, 2, 2.
And so on.
Triangle begins:
3,
5,2,
7,4,3,2,2,
9,5,4,6,3,3,3,3,2,2,2,2,
11,6,5,7,4,8,3,4,4,3,5,3,3,2,2,2,2,2,2,2,2,

Crossrefs

Cf. A135010, A138121, A182735, A182737, A182743, A182747, A182812.

Sequence in context: A164611 A316086 A227988 * A334627 A073897 A237058

Adjacent sequences: A182810 A182811 A182812 * A182814 A182815 A182816

Keyword

nonn,tabf

Author

Omar E. Pol, Dec 04 2010

Status

approved