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A334440
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Irregular triangle T(n,k) read by rows: row n lists numbers of distinct parts of the n-th integer partition in Abramowitz-Stegun (sum/length/lex) order.
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15
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0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 1, 3, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 2, 1, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 3, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 3
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OFFSET
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0,6
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COMMENTS
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The total number of parts, counting duplicates, is A036043. The version for reversed partitions is A103921.
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
0
1
1 1
1 2 1
1 1 2 2 1
1 2 2 2 2 2 1
1 1 2 2 1 3 2 2 2 2 1
1 2 2 2 2 2 3 2 2 3 2 2 2 2 1
1 1 2 2 2 2 2 3 3 2 1 3 2 3 2 2 3 2 2 2 2 1
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MATHEMATICA
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Join@@Table[Length/@Union/@Sort[IntegerPartitions[n]], {n, 0, 10}]
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CROSSREFS
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The number of not necessarily distinct parts is A036043.
The version for reversed partitions is A103921.
Ignoring length (sum/lex) gives A103921 (also).
a(n) is the number of distinct elements in row n of A334301.
The maximum part of the same partition is A334441.
Lexicographically ordered reversed partitions are A026791.
Reversed partitions in Abramowitz-Stegun (sum/length/lex) order are A036036.
Partitions in increasing-length colex order (sum/length/colex) are A036037.
Graded reverse-lexicographically ordered partitions are A080577.
Partitions counted by sum and number of distinct parts are A116608.
Graded lexicographically ordered partitions are A193073.
Partitions in colexicographic order (sum/colex) are A211992.
Partitions in dual Abramowitz-Stegun (sum/length/revlex) order are A334439.
Cf. A001221, A049085, A124734, A185974, A296774, A299755, A334028, A334302, A334433, A334434, A334435, A334438.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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