A220484 Triangle read by rows: T(j,k) is the total number of appearances of the smallest parts in the j-th partition of n, with partitions as nonincreasing lists of parts in lexicographic order.

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

Offset: 1

Author

Omar E. Pol, Jan 20 2013

Keywords

• nonn
• tabf

Comments

The sum of row n equals spt(n) = A092269(n), the smallest part partition function.

Examples

			For n = 5:
------------------------------------------
.                         number of
Partitions of 5         smallest parts
------------------------------------------
1 + 1 + 1 + 1 + 1              5
2 + 1 + 1 + 1                  3
3 + 1 + 1                      2
2 + 2 + 1                      1
4 + 1                          1
3 + 2                          1
5                              1
------------------------------------------
So row 5 is [5, 3, 2, 1, 1, 1, 1]. The sum of row 5 is 5+3+2+1+1+1+1 = spt(5) = A092269(n) = 14.
.
Written as an irregular triangle begins:
1;
2,1;
3,1,1;
4,2,1,2,1;
5,3,2,1,1,1,1;
6,4,3,2,2,1,1,3,1,2,1;
7,5,4,3,3,2,2,1,1,1,1,2,1,1,1;
8,6,5,4,4,3,3,2,2,2,2,1,1,1,1,4,2,1,1,1,2,1;
9,7,6,5,5,4,4,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,3,2,1,1,3,1,1,1;
		

Crossrefs

Column 1 is A000027. Row n has length A000041(n). Row sums give A092269.

Cf. A209514, A220504.