A210971 Triangle read by rows in which row n lists the region number of the parts of the k-th partition of n, with partitions reverse lexicographically ordered.

1, 3, 2, 6, 5, 3, 11, 10, 8, 9, 5, 18, 17, 15, 16, 12, 13, 7, 29, 28, 26, 27, 23, 24, 18, 28, 20, 21, 11

Offset: 1

Author

Omar E. Pol, Jun 30 2012

Keywords

• nonn
• tabf
• more

Comments

Each part of a partition of n belongs to a different region of n. The "region number" of a part of the r-th region of n is equal to r. For the definition of "region of n" see A206437.

Examples

			For n = 5 we have:
------------------------------------------------------
.              Two arrangements             Sum of
k           of the partitions of 5        partition k
------------------------------------------------------
7      [5]                          [5]        5
6      [3+2]                      [3+2]        5
5      [4+1]                    [4  +1]        5
4      [2+1+1]                [2+2  +1]        5
3      [3+1+1]              [3  +1  +1]        5
2      [2+1+1+1]          [2+1  +1  +1]        5
1      [1+1+1+1+1]      [1+1+1  +1  +1]        5
------------------------------------------------------
.              Two arrangements
.           of the region numbers           Sum of
k           of the partitions of 5          zone k
------------------------------------------------------
7      [7]                          [7]        7
6      [6,7]                      [6,7]       13
5      [5,7]                    [5,  7]       12
4      [4,5,7]                [4,5,  7]       16
3      [3,5,7]              [3,  5,  7]       15
2      [2,3,5,7]          [2,3,  5,  7]       17
1      [1,2,3,5,7]      [1,2,3,  5,  7]       18
------------------------------------------------------
So row 5 of triangle gives: 18, 17, 15, 16, 12, 13, 7.
.
Triangle begins:
1;
3,2;
6,5,3;
11,10,8,9,5;
18,17,15,16,12,13,7;
29,28,26,27,23,24,18,28,20,21,11;
		

Links

• Omar E. Pol, Illustration of the seven regions of 5

Crossrefs

Column 1 is A026905. Right border = row lengths = A000041, n>=1. Row sums give A210972.

Cf. A135010, A138121, A182703, A194446, A206437, A210969.