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A308929
Sum of the fifth largest parts in the partitions of n into 7 parts.
7
0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 13, 19, 27, 38, 54, 73, 101, 133, 177, 230, 298, 380, 485, 608, 762, 944, 1165, 1423, 1738, 2101, 2534, 3035, 3625, 4300, 5095, 5996, 7043, 8231, 9598, 11142, 12910, 14893, 17148, 19674, 22529, 25709, 29295, 33267
OFFSET
0,10
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)} l.
a(n) = A308926(n) - A308927(n) - A308928(n) - A308930(n) - A308931(n) - A308932(n) - A308933(n).
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[Sum[l, {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}]
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 30 2019
STATUS
approved