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A308867 Sum of all the parts in the partitions of n into 6 parts.

%I A308867 #10 Oct 29 2024 14:18:29
%S A308867 0,0,0,0,0,0,6,7,16,27,50,77,132,182,280,390,560,748,1044,1349,1800,
%T A308867 2310,2992,3749,4776,5875,7332,8937,10948,13166,15960,18972,22688,
%U A308867 26763,31654,36995,43416,50320,58520,67431,77800,89052,102144,116186,132396,149895
%N A308867 Sum of all the parts in the partitions of n into 6 parts.
%H A308867 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308867 a(n) = 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)} 1.
%F A308867 a(n) = n * A238340(n).
%F A308867 a(n) = A308868(n) + A308869(n) + A306670(n) + A306671(n) + A308872(n) + A308873(n).
%t A308867 Table[n*Sum[Sum[Sum[Sum[Sum[1, {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, 100}]
%t A308867 Table[Total[Flatten[IntegerPartitions[n,{6}]]],{n,0,50}] (* _Harvey P. Dale_, Oct 29 2024 *)
%Y A308867 Cf. A238340, A308868, A308869, A306670, A306671, A308872, A308873.
%K A308867 nonn
%O A308867 0,7
%A A308867 _Wesley Ivan Hurt_, Jun 29 2019