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A326371
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Irregular triangular array: row n shows the number of condensations needed to convert all the partitions of n to strict partitions.
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3
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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
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OFFSET
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1,3
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COMMENTS
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It appears that there is a limiting row and that it includes every positive integer.
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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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 *)
TableForm[t]
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CROSSREFS
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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STATUS
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approved
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