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Sum of the even parts of the partitions of n into 8 parts.
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%I #9 Aug 23 2023 10:58:38

%S 0,0,0,0,0,0,0,0,0,2,4,12,18,38,60,104,152,232,324,472,642,896,1194,

%T 1626,2112,2794,3590,4644,5866,7466,9300,11646,14344,17716,21588,

%U 26374,31822,38462,46034,55130,65440,77726,91604,107990,126434,148006,172238

%N Sum of the even parts of the partitions of n into 8 parts.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} i * ((i-1) mod 2) + j * ((j-1) mod 2) + k * ((k-1) mod 2) + l * ((l-1) mod 2) + m * ((m-1) mod 2) + o * ((o-1) mod 2) + p * ((p-1) mod 2) + (n-i-j-k-l-m-o-p) * ((n-i-j-k-l-m-o-p-1) mod 2).

%t Table[Total[Select[Flatten[IntegerPartitions[n,{8}]],EvenQ]],{n,0,50}] (* _Harvey P. Dale_, Aug 20 2023 *)

%K nonn

%O 0,10

%A _Wesley Ivan Hurt_, Aug 10 2019