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

1,2

Comments

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

Links

Table of n, a(n) for n=1..96.

Example

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.

Sequence in context: A010766 A135841 A210992 * A174066 A089178 A187489

Adjacent sequences: A220481 A220482 A220483 * A220485 A220486 A220487

Keyword

nonn,tabf

Author

Omar E. Pol, Jan 20 2013

Status

approved