A308873 Sum of the largest parts in the partitions of n into 6 parts.

0, 0, 0, 0, 0, 0, 1, 2, 5, 9, 17, 27, 46, 67, 103, 146, 210, 285, 396, 520, 694, 896, 1162, 1466, 1865, 2310, 2881, 3525, 4321, 5215, 6317, 7535, 9011, 10653, 12603, 14761, 17316, 20113, 23390, 26990, 31146, 35698, 40939, 46632, 53139, 60221, 68236, 76931

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, A306671, A308872.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[(n - i - j - k - l - m), {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)} (n-i-j-k-l-m).

a(n) = A308867(n) - A308868(n) - A308869(n) - A306670(n) - A306671(n) - A308872(n).