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A308931 Sum of the third largest parts in the partitions of n into 7 parts.

%I A308931 #13 Mar 17 2025 04:10:40
%S A308931 0,0,0,0,0,0,0,1,1,2,4,7,11,19,28,42,61,88,121,171,228,307,405,531,
%T A308931 682,880,1111,1403,1750,2174,2670,3281,3983,4827,5807,6965,8291,9861,
%U A308931 11641,13718,16080,18804,21881,25423,29392,33921,39001,44753,51163,58411
%N A308931 Sum of the third largest parts in the partitions of n into 7 parts.
%H A308931 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308931 a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} j.
%F A308931 a(n) = A308926(n) - A308927(n) - A308928(n) - A308929(n) - A308930(n) - A308932(n) - A308933(n).
%t A308931 Table[Total[IntegerPartitions[n,{7}][[All,3]]],{n,0,50}] (* _Harvey P. Dale_, Aug 15 2020 *)
%Y A308931 Cf. A026813, A308926, A308927, A308928, A308929, A308930, A308932, A308933.
%K A308931 nonn
%O A308931 0,10
%A A308931 _Wesley Ivan Hurt_, Jun 30 2019