A308989 Sum of all the parts in the partitions of n into 8 parts.

0, 0, 0, 0, 0, 0, 0, 0, 8, 9, 20, 33, 60, 91, 154, 225, 352, 493, 720, 988, 1400, 1869, 2552, 3358, 4464, 5750, 7488, 9504, 12152, 15225, 19140, 23684, 29408, 35970, 44098, 53445, 64836, 77848, 93556, 111423, 132760, 156948, 185514, 217838, 255728, 298350

Offset

0,9

Links

David A. Corneth, Table of n, a(n) for n = 0..10000 (first 101 terms from Harvey P. Dale)

Index entries for sequences related to partitions

Formula

a(n) = n * Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} 1.

a(n) = n * A026814(n).

a(n) = A308990(n) + A308991(n) + A308992(n) + A308994(n) + A308995(n) + A308996(n) + A308997(n) + A308998(n).

Mathematica

Table[Total[Flatten[IntegerPartitions[n, {8}]]], {n, 0, 50}] (* Harvey P. Dale, Jan 12 2022 *)

Crossrefs

Cf. A026814, A308990, A308991, A308992, A308994, A308995, A308996, A308997, A308998.

Sequence in context: A071869 A326444 A309484 * A048124 A322637 A322640

Adjacent sequences: A308986 A308987 A308988 * A308990 A308991 A308992

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jul 04 2019

Status

approved