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%I #10 Sep 12 2021 21:26:26
%S 0,0,0,0,0,0,0,0,1,1,2,4,7,11,19,28,44,63,92,128,183,246,337,448,597,
%T 774,1012,1291,1656,2085,2627,3264,4064,4987,6127,7450,9055,10901,
%U 13126,15669,18701,22157,26228,30858,36279,42397,49509,57527,66773,77148
%N Sum of the third largest 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)} j.
%F a(n) = A308989(n) - A308990(n) - A308991(n) - A308992(n) - A308994(n) - A308995(n) - A308997(n) - A308998(n).
%t Table[Total[IntegerPartitions[n,{8}][[All,3]]],{n,0,50}] (* _Harvey P. Dale_, Jul 19 2020 *)
%Y Cf. A026814, A308989, A308990, A308991, A308992, A308994, A308995, A308997, A308998.
%K nonn
%O 0,11
%A _Wesley Ivan Hurt_, Jul 04 2019
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