1,3

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.

The shell model of partitions can be interpreted as a "Table of Partitions". See also A138121. [From Omar E. Pol (info(AT)polprimos.com), Nov 18 2009]

O. E. Pol, Illustration of the shell model of partitions [From Omar E. Pol (info(AT)polprimos.com), Nov 18 2009]

O. E. Pol, Illustration of the shell model of partitions (2D view) [From Omar E. Pol (info(AT)polprimos.com), Nov 18 2009]

O. E. Pol, Illustration of the shell model of partitions (3D view) [From Omar E. Pol (info(AT)polprimos.com), Nov 18 2009]

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

Cf. A006128, A137138. See A138138 for another version.

Sequence in context: A114118 A146014 A106177 this_sequence A138138 A080209 A127949

Cf. A000041, A026791, A026792, A138121, A138135, A138137, A138879, A138880, A141285, A144120, A144300, A167928. [From Omar E. Pol (info(AT)polprimos.com), Nov 18 2009]

Adjacent sequences: A135007 A135008 A135009 this_sequence A135011 A135012 A135013

nonn,tabf,new

Omar E. Pol (info(AT)polprimos.com), Nov 17 2007, Nov 18 2007, Mar 21 2008