A308928 Sum of the sixth largest parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 12, 17, 24, 33, 46, 61, 84, 109, 144, 184, 237, 298, 379, 470, 585, 719, 882, 1069, 1300, 1560, 1873, 2230, 2653, 3129, 3694, 4326, 5063, 5892, 6848, 7917, 9147, 10513, 12071, 13804, 15765, 17935, 20389, 23088, 26118

Offset: 0

Author

Wesley Ivan Hurt, Jun 30 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A026813, A308926, A308927, A308929, A308930, A308931, A308932, A308933.

Programs

Mathematica

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

a(n) = A308926(n) - A308927(n) - A308929(n) - A308930(n) - A308931(n) - A308932(n) - A308933(n).