%I #5 Aug 12 2019 03:25:48
%S 0,0,0,0,0,0,0,0,0,0,1,2,5,8,15,24,39,58,90,120,170,228,310,404,537,
%T 684,886,1116,1415,1756,2198,2690,3315,4022,4895,5876,7083,8426,10056,
%U 11880,14055,16484,19366,22560,26317,30488,35340,40712,46932,53788,61674
%N Number of even parts in the partitions of n into 9 parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} ((q-1) mod 2) + ((p-1) mod 2) + ((o-1) mod 2) + ((m-1) mod 2) + ((l-1) mod 2) + ((k-1) mod 2) + ((j-1) mod 2) + ((i-1) mod 2) + ((n-i-j-k-l-m-o-p-q-1) mod 2).
%t Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[ Mod[i - 1, 2] + Mod[j - 1, 2] + Mod[k - 1, 2] + Mod[l - 1, 2] + Mod[m - 1, 2] + Mod[o - 1, 2] + Mod[p - 1, 2] + Mod[q - 1, 2] + Mod[n - i - j - k - l - m - o - p - q - 1, 2], {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]
%K nonn
%O 0,12
%A _Wesley Ivan Hurt_, Aug 11 2019