A308931 Sum of the third largest parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 7, 11, 19, 28, 42, 61, 88, 121, 171, 228, 307, 405, 531, 682, 880, 1111, 1403, 1750, 2174, 2670, 3281, 3983, 4827, 5807, 6965, 8291, 9861, 11641, 13718, 16080, 18804, 21881, 25423, 29392, 33921, 39001, 44753, 51163, 58411

Offset: 0

Author

Wesley Ivan Hurt, Jun 30 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A026813, A308926, A308927, A308928, A308929, A308930, A308932, A308933.

Programs

Mathematica

Table[Total[IntegerPartitions[n,{7}][[All,3]]],{n,0,50}] (* Harvey P. Dale, Aug 15 2020 *)

Formula

a(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)} j.

a(n) = A308926(n) - A308927(n) - A308928(n) - A308929(n) - A308930(n) - A308932(n) - A308933(n).