A182715 - OEIS

A182715

Triangle read by rows in which row n lists in nonincreasing order the smallest part of every partition of n.

0, 1, 2, 1, 3, 1, 1, 4, 2, 1, 1, 1, 5, 2, 1, 1, 1, 1, 1, 6, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 7, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

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OFFSET

0,3

COMMENTS

Triangle read by rows in which row n lists the smallest parts of all partitions of n in the order produced by the shell model of partitions of A138121.

Also, row n lists the "filler parts" of all partition of n. For more information see A182699.

Row n has length A000041(n). Row sums give A046746. Column 1 gives A001477. The last A000041(n-1) terms of row n are ones, n >= 1.

LINKS

Table of n, a(n) for n=0..84.

Omar E. Pol, Illustration of the smallest parts of all partitions of 10 (colored blue) in the shell model of partitions

EXAMPLE

For row 10, see the illustration of the link.

Triangle begins:

2,1,

3,1,1,

4,2,1,1,1,

5,2,1,1,1,1,1,