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A163986 Sum of all repeated parts of all partitions of n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

See A163985 for more information.

LINKS

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)

FORMULA

a(0)=0, a(n)=A066186(n)-A163985(n), for n>0.

EXAMPLE

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.

MATHEMATICA

Table[Total[Flatten[Select[Split[Sort[Flatten[IntegerPartitions[n]]]], Length[ #]>1&]]], {n, 0, 50}] (* Harvey P. Dale, Apr 30 2018 *)

CROSSREFS

Cf. A000041, A066186, A163985.

Sequence in context: A082015 A018263 A018587 * A189583 A153936 A027301

Adjacent sequences:  A163983 A163984 A163985 * A163987 A163988 A163989

KEYWORD

easy,nonn

AUTHOR

Omar E. Pol, Aug 14 2009

EXTENSIONS

More terms from Alois P. Heinz, Jan 30 2011

STATUS

approved

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Last modified June 20 10:00 EDT 2021. Contains 345162 sequences. (Running on oeis4.)