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A241825
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Number of partitions p = [x(1), ..., x(k)], where x(1) >= x(2) >= ... >= x(k), of n such that min(x(i) - x(i-1)) = number of distinct parts of p.
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6
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0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 11, 10, 13, 13, 17, 17, 21, 22, 27, 28, 33, 35, 41, 43, 49, 52, 59, 62, 69, 73, 81, 85, 93, 98, 107, 112, 121, 128, 138, 145, 156, 165, 178, 188, 202
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OFFSET
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0,13
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LINKS
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FORMULA
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EXAMPLE
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a(6) counts this single partition: 42.
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MATHEMATICA
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z = 30; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := d[p] = Length[DeleteDuplicates[p]]; g1[p_] := Min[-Differences[p]]
Table[Count[f[n], p_ /; g1[p] < d[p]], {n, 0, z}] (* A241823 *)
Table[Count[f[n], p_ /; g1[p] <= d[p]], {n, 0, z}] (* A241824 *)
Table[Count[f[n], p_ /; g1[p] == d[p]], {n, 0, z}] (* A241825 *)
Table[Count[f[n], p_ /; g1[p] >= d[p]], {n, 0, z}] (* A241826 *)
Table[Count[f[n], p_ /; g1[p] > d[p]], {n, 0, z}] (* A241827 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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