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

1,6

Links

Table of n, a(n) for n=1..86.

Example

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.

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]

Crossrefs

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

Sequence in context: A219311 A363393 A022880 * A128097 A328096 A353778

Adjacent sequences: A366611 A366612 A366613 * A366615 A366616 A366617

Keyword

nonn,tabf

Author

Clark Kimberling, Oct 25 2023

Status

approved