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Number of even parts in the partitions of n into 10 parts.
0

%I #5 Aug 12 2019 03:26:18

%S 0,0,0,0,0,0,0,0,0,0,0,1,2,5,8,15,24,39,58,90,130,179,246,335,446,592,

%T 770,997,1278,1625,2046,2569,3194,3950,4856,5943,7226,8756,10548,

%U 12661,15134,18016,21360,25256,29744,34924,40872,47704,55504,64421,74554

%N Number of even 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)} ((r-1) mod 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-r-1) mod 2).

%t Table[Sum[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[r - 1, 2] + Mod[n - i - j - k - l - m - o - p - q - r - 1, 2], {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, 80}]

%K nonn

%O 0,13

%A _Wesley Ivan Hurt_, Aug 11 2019