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A362208
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Irregular triangle read by rows: T(n, k) is the number of compositions (ordered partitions) of n into exactly k distinct parts between the members of [k^2].
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2
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1, 0, 0, 2, 0, 2, 0, 4, 0, 2, 6, 0, 2, 6, 0, 0, 12, 0, 0, 18, 0, 0, 24, 24, 0, 0, 30, 24, 0, 0, 42, 48, 0, 0, 42, 72, 0, 0, 48, 120, 0, 0, 48, 144, 120, 0, 0, 48, 216, 120, 0, 0, 42, 264, 240, 0, 0, 42, 360, 360, 0, 0, 30, 432, 600, 0, 0, 24, 552, 840, 0, 0, 18, 648, 1200, 720
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OFFSET
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1,4
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LINKS
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EXAMPLE
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The irregular triangle begins:
1;
0;
0, 2;
0, 2;
0, 4;
0, 2, 6;
0, 2, 6;
0, 0, 12;
0, 0, 18;
0, 0, 24, 24;
0, 0, 30, 24;
0, 0, 42, 48;
0, 0, 42, 72;
0, 0, 48, 120;
0, 0, 48, 144, 120;
...
T(7,3) = 6 since we have: 1+2+4, 1+4+2, 2+1+4, 2+4+1, 4+1+2, 4+2+1.
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MATHEMATICA
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Flatten[Table[Length[Select[Join@@Permutations/@Select[IntegerPartitions[n, All, Range[k^2]], UnsameQ@@#&], Length[#]==k&]], {n, 21}, {k, Floor[(Sqrt[8n+1]-1)/2]}]] (* After Gus Wiseman in A072574 *)
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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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