|
Search: id:A135010
|
|
|
| A135010 |
|
A shell model of partitions. Triangle read by rows: row n lists the parts of the outer shell of the partitions of n. |
|
+0
17
|
|
| 1, 1, 2, 1, 1, 3, 1, 1, 1, 2, 2, 4, 1, 1, 1, 1, 1, 2, 3, 5, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 3, 3, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 2, 5, 3, 4, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 4, 2, 3, 3, 2, 6, 3, 5, 4, 4, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
The set of partitions of n contains all partitions of the previous numbers. The number of shell of the partitions of n is equal to n. The number of parts of the outer shell of the partitions of n is A138137(n)=A006128(n)-A006128(n-1) and equal to the number of terms of row n. The number of terms of row n that are equal to 1 is A000041(n-1). The shell model of partitions has several 2D and 3D models. In this sequence the last term of row n is n.
|
|
EXAMPLE
|
Triangle begins:
1
1,2
1,1,3
1,1,1,2,2,4
1,1,1,1,1,2,3,5
1,1,1,1,1,1,1,2,2,2,2,4,3,3,6
1,1,1,1,1,1,1,1,1,1,1,2,2,3,2,5,3,4,7
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,4,2,3,3,2,6,3,5,4,4,8
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,2,2,5,2,3,4,2,7,3,3,3,3,6,4,5,9
|
|
CROSSREFS
|
Cf. A006128, A137138. See A138138 for another version.
Adjacent sequences: A135007 A135008 A135009 this_sequence A135011 A135012 A135013
Sequence in context: A114118 A146014 A106177 this_sequence A138138 A080209 A127949
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
Omar E. Pol (info(AT)polprimos.com), Nov 17 2007, Nov 18 2007, Mar 21 2008
|
|
|
Search completed in 0.002 seconds
|
