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A326596
Sum of the third largest parts of the partitions of n into 10 parts.
10
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 7, 11, 19, 28, 44, 65, 96, 134, 194, 265, 367, 496, 670, 883, 1173, 1521, 1980, 2537, 3248, 4104, 5194, 6488, 8101, 10025, 12387, 15175, 18582, 22570, 27385, 33020, 39745, 47569, 56861, 67602, 80253, 94849, 111914
OFFSET
0,13
FORMULA
a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} j.
a(n) = A326588(n) - A326589(n) - A326590(n) - A326591(n) - A326592(n) - A326593(n) - A326594(n) - A326595(n) - A326597(n) - A326598(n).
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[j, {i, j, Floor[(n - j - k - l - m - o - p - q - r)/2]}], {j, k, Floor[(n - k - l - m - o - p - q - r)/3]}], {k, l, Floor[(n - l - m - o - p - q - r)/4]}], {l, m, Floor[(n - m - o - p - q - r)/5]}], {m, o, Floor[(n - o - p - q - r)/6]}], {o, p, Floor[(n - p - q - r)/7]}], {p, q, Floor[(n - q - r)/8]}], {q, r, Floor[(n - r)/9]}], {r, Floor[n/10]}], {n, 0, 50}]
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 13 2019
STATUS
approved