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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

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Last modified January 8 02:43 EST 2009. Contains 152824 sequences.


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