A326595 - OEIS

%I #8 Jul 14 2019 06:32:23

%S 0,0,0,0,0,0,0,0,0,0,1,1,2,3,6,9,15,22,35,50,75,103,149,202,281,376,

%T 510,669,889,1149,1499,1913,2453,3093,3917,4886,6106,7544,9330,11419,

%U 13989,16979,20614,24837,29912,35785,42790,50857,60399,71360,84233,98952

%N Sum of the fourth largest parts of 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)} k.

%F a(n) = A326588(n) - A326589(n) - A326590(n) - A326591(n) - A326592(n) - A326593(n) - A326594(n) - A326596(n) - A326597(n) - A326598(n).

%t Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[k, {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, A326592, A326593, A326594, A326596, A326597, A326598.

%K nonn

%O 0,13

%A _Wesley Ivan Hurt_, Jul 13 2019