A308869 Sum of the fifth largest parts in the partitions of n into 6 parts.

0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 13, 17, 25, 34, 48, 63, 86, 109, 143, 182, 232, 288, 363, 442, 547, 662, 804, 961, 1157, 1368, 1626, 1909, 2245, 2613, 3054, 3525, 4082, 4688, 5388, 6150, 7031, 7974, 9059, 10231, 11560, 12991, 14614, 16346, 18300, 20400

Offset: 0

Author

Wesley Ivan Hurt, Jun 29 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A238340, A308867, A308868, A306670, A306671, A308872, A308873.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[l, {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)} l.

a(n) = A308867(n) - A308868(n) - A306670(n) - A306671(n) - A308872(n) - A308873(n).