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A308870 Sum of the fourth largest parts in the partitions of n into 6 parts.

%I A308870 #9 Jul 30 2024 13:29:21
%S A308870 0,0,0,0,0,0,1,1,2,3,6,9,15,20,31,42,61,80,112,143,191,243,316,393,
%T A308870 501,613,767,930,1141,1367,1659,1967,2354,2769,3279,3824,4491,5196,
%U A308870 6047,6956,8031,9181,10536,11971,13647,15434,17497,19690,22211,24880,27929
%N A308870 Sum of the fourth largest parts in the partitions of n into 6 parts.
%H A308870 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308870 a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} k.
%F A308870 a(n) = A308867(n) - A308868(n) - A308869(n) - A306671(n) - A308872(n) - A308873(n).
%t A308870 Table[Sum[Sum[Sum[Sum[Sum[k, {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]
%t A308870 Table[Total[IntegerPartitions[n,{6}][[;;,4]]],{n,0,50}] (* _Harvey P. Dale_, Jul 30 2024 *)
%Y A308870 Cf. A238340, A308867, A308868, A308869, A306671, A308872, A308873.
%K A308870 nonn
%O A308870 0,9
%A A308870 _Wesley Ivan Hurt_, Jun 29 2019