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A246688
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Triangle in which n-th row lists lexicographically ordered increasing lists of parts of all partitions of n into distinct parts.
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20
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1, 2, 1, 2, 3, 1, 3, 4, 1, 4, 2, 3, 5, 1, 2, 3, 1, 5, 2, 4, 6, 1, 2, 4, 1, 6, 2, 5, 3, 4, 7, 1, 2, 5, 1, 3, 4, 1, 7, 2, 6, 3, 5, 8, 1, 2, 6, 1, 3, 5, 1, 8, 2, 3, 4, 2, 7, 3, 6, 4, 5, 9, 1, 2, 3, 4, 1, 2, 7, 1, 3, 6, 1, 4, 5, 1, 9, 2, 3, 5, 2, 8, 3, 7, 4, 6, 10
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OFFSET
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1,2
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LINKS
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EXAMPLE
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Triangle begins:
[1];
[2];
[1,2], [3];
[1,3], [4];
[1,4], [2,3], [5];
[1,2,3], [1,5], [2,4], [6];
[1,2,4], [1,6], [2,5], [3,4], [7];
[1,2,5], [1,3,4], [1,7], [2,6], [3,5], [8];
[1,2,6], [1,3,5], [1,8], [2,3,4], [2,7], [3,6], [4,5], [9];
[1,2,3,4], [1,2,7], [1,3,6], [1,4,5], [1,9], [2,3,5], [2,8], [3,7], [4,6], [10];
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MAPLE
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b:= proc(n, i) b(n, i):= `if`(n=0, [[]], `if`(i>n, [],
[map(x->[i, x[]], b(n-i, i+1))[], b(n, i+1)[]]))
end:
T:= n-> map(x-> x[], b(n, 1))[]:
seq(T(n), n=1..12);
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MATHEMATICA
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T[n_] := Module[{ip, lg}, ip = Reverse /@ Select[ IntegerPartitions[n], # == DeleteDuplicates[#]&]; lg = Length /@ ip // Max; SortBy[PadRight[#, lg]&][ip]];
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CROSSREFS
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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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