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A326371
Irregular triangular array: row n shows the number of condensations needed to convert all the partitions of n to strict partitions.
3
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
1,3
COMMENTS
It appears that there is a limiting row and that it includes every positive integer.
LINKS
EXAMPLE
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
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]
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Clark Kimberling, Jul 06 2019
STATUS
approved