A309664 - OEIS

%I #7 Nov 01 2020 12:44:29

%S 0,0,0,0,0,0,0,0,0,0,0,2,4,12,18,38,60,104,152,250,360,524,726,1032,

%T 1396,1928,2546,3418,4466,5862,7526,9742,12352,15710,19692,24742,

%U 30682,38110,46792,57504,70046,85258,102964,124366,149128,178694,212828,253286

%N Sum of the 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 * ((r-1) mod 2) + q * ((q-1) mod 2) + p * ((p-1) mod 2) + o * ((o-1) mod 2) + m * ((m-1) mod 2) + l * ((l-1) mod 2) + k * ((k-1) mod 2) + j * ((j-1) mod 2) + i * ((i-1) mod 2) + (n-i-j-k-l-m-o-p-q-r-1) * ((n-i-j-k-l-m-o-p-q-r-1) mod 2).

%t Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[i * Mod[i - 1, 2] + j * Mod[j - 1, 2] + k * Mod[k - 1, 2] + l * Mod[l - 1, 2] + m * Mod[m - 1, 2] + o * Mod[o - 1, 2] + p * Mod[p - 1, 2] + q * Mod[q - 1, 2] + r * Mod[r - 1, 2] + (n - i - j - k - l - m - o - p - q - r) * 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, 50}]

%t Table[Total[Select[Flatten[IntegerPartitions[n,{10}]],EvenQ]],{n,0,50}] (* _Harvey P. Dale_, Nov 01 2020 *)

%K nonn

%O 0,12

%A _Wesley Ivan Hurt_, Aug 11 2019