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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. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A187489 A116599 A138121 * A207378 A166556 A275257

Adjacent sequences:  A138148 A138149 A138150 * A138152 A138153 A138154

KEYWORD

nonn,tabf,less,changed

AUTHOR

Omar E. Pol, Mar 21 2008

STATUS

approved

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Last modified May 29 09:48 EDT 2020. Contains 334698 sequences. (Running on oeis4.)