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%I #9 Nov 21 2022 17:36:43
%S 0,0,0,0,0,0,0,0,8,7,16,21,42,53,94,121,200,261,396,516,758,973,1358,
%T 1732,2352,2956,3898,4860,6286,7759,9840,12038,15064,18254,22510,
%U 27071,33014,39386,47522,56293,67320,79222,93910,109848,129294,150344,175706
%N Sum of the odd parts in 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 mod 2) + j * (j mod 2) + k * (k mod 2) + l * (l mod 2) + m * (m mod 2) + o * (o mod 2) + p * (p mod 2) + (n-i-j-k-l-m-o-p) * ((n-i-j-k-l-m-o-p) mod 2).
%t Table[Total[Select[Flatten[IntegerPartitions[n,{8}]],OddQ]],{n,0,50}] (* _Harvey P. Dale_, Nov 20 2022 *)
%K nonn
%O 0,9
%A _Wesley Ivan Hurt_, Aug 10 2019
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