A326371 Irregular triangular array: row n shows the number of condensations needed to convert all the partitions of n to strict partitions.

1, 1, 2, 1, 1, 2, 1, 1, 2, 3, 2, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 2, 1, 3, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 3, 4, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 1, 2, 3, 2, 2, 2, 2

Offset: 1

Author

Clark Kimberling, Jul 06 2019

Keywords

• nonn
• tabf
• easy

Comments

It appears that there is a limiting row and that it includes every positive integer.

Examples

			First seven rows:
1
1   2
1   1   2
1   1   2   3   2
1   1   1   2   2   2   2
1   1   1   2   2   1   3   2   2   2   2
1   1   1   2   1   1   2   2   2   3   2   2   2   2   2
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000009, A000041, A239312, A326370.

Programs

Mathematica

f[m_] := Table[Tally[m][[h]][[1]]*Tally[m][[h]][[2]], {h, 1, Length[Tally[m]]}];l
m[n_, k_] := IntegerPartitions[n][[k]];
q[n_, k_] := -1 + Length[FixedPointList[f, m[n, k]]];
t = Table[q[n, k], {n, 1, 16}, {k, 1, PartitionsP[n]}]   (* A326371, array *)
Flatten[t]   (* A326371, sequence *)
TableForm[t]