A138151 A shell model of partitions. Triangle read by rows: row n lists the parts of the last section of the set of partitions of n.

1, 2, 1, 3, 1, 1, 4, 2, 2, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 1, 6, 4, 2, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 7, 5, 2, 4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 6, 2, 5, 3, 4, 4, 4, 2, 2, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 7, 2, 6, 3, 5, 4, 5, 2, 2, 4, 3, 2, 3, 3, 3, 3, 2, 2

Offset

1,2

Comments

Row n lists the terms of row n of A138138, in decreasing order. See the integrated diagram of partitions and more information in the entry A138138.

Links

Robert Price, Table of n, a(n) for n = 1..4630, 20 rows.

Example

Triangle begins:
1
2,1
3,1,1
4,2,2,1,1,1
5,3,2,1,1,1,1,1,
6,4,2,3,3,2,2,2,1,1,1,1,1,1,1
7,5,2,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1
8,6,2,5,3,4,4,4,2,2,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
9,7,2,6,3,5,4,5,2,2,4,3,2,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

Mathematica

Table[Cases[IntegerPartitions[n], x_ /; Last[x] != 1] ~Join~ConstantArray[{1}, PartitionsP[n - 1]], {n, 8}] // Flatten (* Robert Price, May 22 2020 *)

Crossrefs

Cf. A135010, A138121, A138122, A138123, A138136, A138137, A138138, A138152, A138153.

Sequence in context: A355145 A116599 A138121 * A207378 A166556 A275257

Adjacent sequences: A138148 A138149 A138150 * A138152 A138153 A138154

Keyword

nonn,tabf,less

Author

Omar E. Pol, Mar 21 2008

Status

approved