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A163986
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Sum of all repeated parts of all partitions of n.
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1
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0, 0, 2, 4, 13, 26, 55, 92, 161, 253, 401, 595, 901, 1288, 1863, 2611, 3665, 5016, 6895, 9273, 12501, 16591, 22001, 28820, 37753, 48901, 63285, 81217, 104049, 132328, 168061, 212041, 267105, 334654, 418473, 520836, 647101, 800496, 988495, 1216138, 1493441, 1827822, 2233225, 2720138, 3307613, 4010941, 4855577, 5863345, 7069009, 8502628, 10211201
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OFFSET
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0,3
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COMMENTS
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See A163985 for more information.
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LINKS
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Table of n, a(n) for n=0..50.
Omar E. Pol, Illustration of the shell model of partitions (2D view)
Omar E. Pol, Illustration of the shell model of partitions (3D view)
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FORMULA
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a(0)=0, a(n)=A066186(n)-A163985(n), for n>0.
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EXAMPLE
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For n=4, the five partitions of 4 are {(4);(2,2);(3,1);(2,1,1);(1,1,1,1)}. Since 1 and 2 are repeated parts and 3 and 4 are not repeated parts (or isolated parts) then a(4)={(2+2)+(1)+(2+1+1)+(1+1+1+1)}=13.
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MATHEMATICA
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Table[Total[Flatten[Select[Split[Sort[Flatten[IntegerPartitions[n]]]], Length[ #]>1&]]], {n, 0, 50}] (* Harvey P. Dale, Apr 30 2018 *)
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CROSSREFS
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Cf. A000041, A066186, A163985.
Sequence in context: A360397 A018263 A018587 * A189583 A153936 A027301
Adjacent sequences: A163983 A163984 A163985 * A163987 A163988 A163989
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KEYWORD
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easy,nonn
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AUTHOR
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Omar E. Pol, Aug 14 2009
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EXTENSIONS
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More terms from Alois P. Heinz, Jan 30 2011
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STATUS
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approved
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