A366614 Irregular triangular array, read by rows: row n gives the numbers max(p) - min(p), in nondecreasing order, where p ranges through the strict partitions p of n.

0, 0, 0, 1, 0, 2, 0, 1, 3, 0, 2, 2, 4, 0, 1, 3, 3, 5, 0, 2, 3, 4, 4, 6, 0, 1, 2, 3, 4, 5, 5, 7, 0, 2, 3, 3, 4, 4, 5, 6, 6, 8, 0, 1, 3, 3, 4, 4, 5, 5, 6, 7, 7, 9, 0, 2, 2, 4, 4, 4, 5, 5, 5, 6, 6, 7, 8, 8, 10, 0, 1, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 9, 9

Offset: 1

Author

Clark Kimberling, Oct 25 2023

Keywords

• nonn
• tabf

Examples

			First twelve rows:
     0
     0
     0   1
     0   2
     0   1   3
     0   2   2   4
     0   1   3   3   5
     0   2   3   4   4   6
     0   1   2   3   4   5   5   7
     0   2   3   3   4   4   5   6   6   8
     0   1   3   3   4   4   5   5   6   7   7   9
     0   2   2   4   4   4   5   5   5   6   6   7   8   8   10
The strict partitions p of 8 are 8, 71, 62, 53, 521, 431, for which max(p)-min(p) are the numbers 0, 6, 4, 2, 4, 3, or, in nondecreasing order, 0, 2, 3, 4, 4, 6, as in row 8.
		

Crossrefs

Cf. A000009 (strict partitions), A117454 (frequencies).

Programs

Mathematica

z = 20; d[n_] := d[n] = Select[IntegerPartitions[n], DeleteDuplicates[#] == # &];
p[n_, k_] := p[n, k] = d[n][[k]];
t = Table[Max[p[n, k]] - Min[p[n, k]], {n, 1, z}, {k, 1, PartitionsQ[n]}]
m = Map[Sort, t]
Column[m]
Flatten[m]