A308933 Sum of the largest parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 9, 17, 27, 46, 69, 106, 153, 222, 307, 430, 577, 778, 1023, 1343, 1726, 2221, 2805, 3540, 4408, 5475, 6722, 8244, 10004, 12116, 14557, 17447, 20758, 24656, 29090, 34254, 40115, 46878, 54512, 63276, 73112, 84322, 96875, 111089

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, A308931, A308932.

Programs

Mathematica

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

a(n) = A308926(n) - A308927(n) - A308928(n) - A308929(n) - A308930(n) - A308931(n) - A308932(n).