A308871 Sum of the third largest parts in the partitions of n into 6 parts.

0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 7, 11, 19, 26, 40, 57, 81, 109, 153, 198, 264, 342, 442, 556, 710, 875, 1093, 1338, 1638, 1975, 2398, 2855, 3416, 4040, 4779, 5595, 6573, 7627, 8875, 10244, 11822, 13549, 15553, 17707, 20187, 22883, 25935, 29239, 32991, 37010

Offset: 0

Author

Wesley Ivan Hurt, Jun 29 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A238340, A308867, A308868, A308869, A306670, A308872, A308873.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[j, {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]

Formula

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

a(n) = A308867(n) - A308868(n) - A308869(n) - A306670(n) - A308872(n) - A308873(n).