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A241061
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Number of partitions p of n into distinct parts such that max(p) < 1 + 2*min(p).
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5
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0, 1, 1, 2, 1, 2, 2, 2, 2, 4, 2, 3, 4, 4, 4, 5, 4, 6, 7, 6, 6, 8, 8, 9, 10, 10, 10, 12, 12, 14, 16, 14, 16, 18, 18, 20, 22, 23, 24, 26, 26, 28, 32, 32, 35, 38, 38, 40, 44, 45, 48, 52, 54, 58, 62, 62, 66, 71, 74, 78, 84, 86, 92, 98, 100, 106, 112, 116, 122
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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a(10) counts these 4 partitions: {10}, {6,4].
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MATHEMATICA
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z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
Table[Count[f[n], p_ /; Max[p] < 1 + 2*Min[p]], {n, 0, z}] (* A241061 *)
Table[Count[f[n], p_ /; Max[p] <= 1 + 2*Min[p]], {n, 0, z}](* A207642 *)
Table[Count[f[n], p_ /; Max[p] == 1 + 2*Min[p]], {n, 0, z}](* A241062 *)
Table[Count[f[n], p_ /; Max[p] >= 1 + 2*Min[p]], {n, 0, z}](* A241037 *)
Table[Count[f[n], p_ /; Max[p] > 1 + 2*Min[p]], {n, 0, z}] (* A241064 *)
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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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