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A240451
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Number of partitions p of n such that (sum of parts with multiplicity 1) > (sum of all other parts).
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5
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0, 1, 1, 2, 2, 4, 5, 8, 10, 17, 20, 28, 35, 55, 66, 87, 106, 153, 183, 243, 293, 401, 477, 608, 723, 984, 1162, 1458, 1720, 2245, 2624, 3301, 3864, 4963, 5775, 7108, 8246, 10508, 12153, 14834, 17125, 21442, 24651, 30028, 34477, 42599, 48778, 58742, 67091
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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(6) counts these 5 partitions: 6, 51, 42, 411, 321.
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MATHEMATICA
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z = 30; p[n_] := p[n] = IntegerPartitions[n]; f[p_] := f[p] = First[Transpose[p]];
ColumnForm[t = Table[Select[p[n], 2 Total[f[Select[#, Last[#] == 1 &] /. {} -> {{0, 0}}]] &[Tally[#]] < n &], {n, 0, z}]] (* shows the partitions *)
ColumnForm[t = Table[Select[p[n], 2 Total[f[Select[#, Last[#] == 1 &] /. {} -> {{0, 0}}]] &[Tally[#]] <= n &], {n, 0, z}]] (* shows the partitions *)
ColumnForm[t = Table[Select[p[n], 2 Total[f[Select[#, Last[#] == 1 &] /. {} -> {{0, 0}}]] &[Tally[#]] == n &], {n, 0, z}]] (* shows the partitions *)
Map[Length, t] (* A240447 with alternating 0's *)
ColumnForm[t = Table[Select[p[n], 2 Total[f[Select[#, Last[#] == 1 &] /. {} -> {{0, 0}}]] &[Tally[#]] > n &], {n, 0, z}]] (* shows the partitions *)
ColumnForm[t = Table[Select[p[n], 2 Total[f[Select[#, Last[#] == 1 &] /. {} -> {{0, 0}}]] &[Tally[#]] >= n &], {n, 0, z}]] (* shows the partitions *)
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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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