A308926 Sum of all the parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 7, 8, 18, 30, 55, 84, 143, 210, 315, 448, 646, 882, 1235, 1640, 2205, 2882, 3772, 4824, 6200, 7800, 9828, 12208, 15138, 18540, 22723, 27520, 33297, 39950, 47845, 56844, 67488, 79534, 93600, 109520, 127920, 148638, 172473, 199144, 229590

Offset: 0

Author

Wesley Ivan Hurt, Jun 30 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A026813, A308927, A308928, A308929, A308930, A308931, A308932, A308933.

Programs

Mathematica

Table[Total[Flatten[IntegerPartitions[n,{7}]]],{n,0,50}] (* Harvey P. Dale, Jul 27 2025 *)

Formula

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

a(n) = n * A026813(n).

a(n) = A308927(n) + A308928(n) + A308929(n) + A308930(n) + A308931(n) + A308932(n) + A308933(n).