A230440 Triangle read by rows in which row n lists A000041(n-1) 1's followed by the list of partitions of n that do not contain 1 as a part in colexicographic order.

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

Offset: 1

Author

Omar E. Pol, Oct 18 2013

Keywords

• nonn
• tabf

Comments

The n-th row of triangle lists the parts of the n-th section of the set of partitions of any integer >= n. For the definition of "section" see A135010.

Examples

			Illustration of initial terms (row = 1..6). The table shows the six sections of the set of partitions of 6 in three ways. Note that before the dissection, the set of partitions was in colexicographic order, see A211992. More generally, in a master model, the six sections of the set of partitions of 6 also can be interpreted as the first six sections of the set of partitions of any integer >= 6.
---------------------------------------------------------
n  j     Diagram          Parts              Parts
---------------------------------------------------------
.         _
1  1     |_|              1;                 1;
.           _
2  1      _| |              1,                 1,
2  2     |_ _|              2;               2;
.             _
3  1         | |              1,                 1,
3  2      _ _| |              1,               1,
3  3     |_ _ _|              3;             3;
.               _
4  1           | |              1,                 1,
4  2           | |              1,               1,
4  3      _ _ _| |              1,             1,
4  4     |_ _|   |            2,2,           2,2,
4  5     |_ _ _ _|              4;           4;
.                 _
5  1             | |              1,                 1,
5  2             | |              1,               1,
5  3             | |              1,             1,
5  4             | |              1,             1,
5  5      _ _ _ _| |              1,           1,
5  6     |_ _ _|   |            3,2,         3,2,
5  7     |_ _ _ _ _|              5;         5;
.                   _
6  1               | |              1,                 1,
6  2               | |              1,               1,
6  3               | |              1,             1,
6  4               | |              1,             1,
6  5               | |              1,           1,
6  6               | |              1,           1,
6  7      _ _ _ _ _| |              1,         1,
6  8     |_ _|   |   |          2,2,2,       2,2,2,
6  9     |_ _ _ _|   |            4,2,       4,2,
6  10    |_ _ _|     |            3,3,       3,3,
6  11    |_ _ _ _ _ _|              6;       6;
...
Triangle begins:
[1];
[1],[2];
[1],[1],[3];
[1],[1],[1],[2,2],[4];
[1],[1],[1],[1],[1],[3,2],[5];
[1],[1],[1],[1],[1],[1],[1],[2,2,2],[4,2],[3,3],[6];
...
		

Crossrefs

Positive terms of A228716.

Row n has length A138137(n).

Row sums give A138879.

Right border gives A000027.

Cf. A000041, A135010, A138121, A141285, A182703, A187219, A193870, A194446, A206437, A207031, A207034, A207383, A207379, A211009.