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A279036
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Number of partitions p of n that contain a proper partition of the maximal part of p.
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0
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0, 0, 0, 1, 1, 4, 4, 10, 12, 21, 25, 46, 50, 82, 99, 148, 175, 259, 303, 435, 513, 708, 845, 1146, 1347, 1802, 2138, 2793, 3318, 4273, 5050, 6471, 7621, 9641, 11406, 14210, 16758, 20833, 24475, 30143
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OFFSET
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1,6
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LINKS
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EXAMPLE
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a(8) counts these 10 partitions: [4,3,1], [4,2,2], [4,2,1,1], [4,1,1,1,1], [3,2,2,1], [3,2,1,1,1], [3,1,1,1,1,1], [2,2,2,1,1], [2,2,1,1,1,1],[2,1,1,1,1,1,1]; e.g., [3,1] is a proper partition of 4.
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MATHEMATICA
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Table[parts = IntegerPartitions[z]; parts = Drop[parts,
Position[Map[#[[1]] &, parts], Floor[z/2], 1, 1][[1]][[1]] - 1];
Count[Table[{first, rest} = {First[#], Rest[#]} &[parts[[nn]]];
Apply[Or, Map[MatchQ[rest, #] &, Map[Flatten[{___, #, ___}] &,
Rest[IntegerPartitions[first]]]]], {nn, Length[parts]}], True], {z, 30}]
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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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