A326592 - OEIS

%I #8 Jul 14 2019 06:32:00

%S 0,0,0,0,0,0,0,0,0,0,1,1,2,3,5,7,11,16,24,34,49,66,92,123,167,220,293,

%T 380,497,636,818,1035,1312,1642,2059,2551,3162,3884,4769,5806,7068,

%U 8539,10310,12370,14826,17670,21038,24920,29482,34725,40848,47852,55989

%N Sum of the seventh largest parts in the partitions of n into 10 parts.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F 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)} o.

%F a(n) = A326588(n) - A326589(n) - A326590(n) - A326591(n) - A326593(n) - A326594(n) - A326595(n) - A326596(n) - A326597(n) - A326598(n).

%t Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[o, {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}]

%Y Cf. A026816, A326588, A326589, A326590, A326591, A326593, A326594, A326595, A326596, A326597, A326598.

%K nonn

%O 0,13

%A _Wesley Ivan Hurt_, Jul 13 2019