|
%I #8 Jul 14 2019 06:32:30
%S 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,
%T 670,883,1173,1521,1980,2537,3248,4104,5194,6488,8101,10025,12387,
%U 15175,18582,22570,27385,33020,39745,47569,56861,67602,80253,94849,111914
%N Sum of the third 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)} j.
%F a(n) = A326588(n) - A326589(n) - A326590(n) - A326591(n) - A326592(n) - A326593(n) - A326594(n) - A326595(n) - A326597(n) - A326598(n).
%t 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}]
%Y Cf. A026816, A326588, A326589, A326590, A326591, A326592, A326593, A326594, A326595, A326597, A326598.
%K nonn
%O 0,13
%A _Wesley Ivan Hurt_, Jul 13 2019
|
