A308930 Sum of the fourth largest parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 6, 9, 15, 22, 33, 46, 67, 91, 128, 169, 228, 297, 390, 498, 641, 806, 1018, 1263, 1569, 1921, 2358, 2856, 3460, 4151, 4978, 5915, 7030, 8287, 9763, 11425, 13357, 15526, 18030, 20825, 24027, 27597, 31660, 36167, 41276, 46921

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, A308931, A308932, A308933.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[k, {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]

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)} k.

a(n) = A308926(n) - A308927(n) - A308928(n) - A308929(n) - A308931(n) - A308932(n) - A308933(n).