The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #10 Sep 13 2019 09:41:13
%S 0,0,0,0,0,1,2,5,9,17,27,44,64,96,134,188,251,339,439,571,724,917,
%T 1137,1411,1719,2097,2519,3023,3586,4253,4990,5848,6797,7891,9092,
%U 10467,11966,13670,15526,17612,19880,22417,25159,28209,31502,35145,39061,43375
%N Sum of the largest parts of the partitions of n into 5 parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-l)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} (n-i-j-k-l).
%F a(n) = A308822(n) - A308823(n) - A308824(n) - A308825(n) - A308826(n).
%e The partitions of n into 5 parts for n = 10, 11, ..
%e 1+1+1+1+10
%e 1+1+1+2+9
%e 1+1+1+3+8
%e 1+1+1+4+7
%e 1+1+1+5+6
%e 1+1+1+1+9 1+1+2+2+8
%e 1+1+1+2+8 1+1+2+3+7
%e 1+1+1+3+7 1+1+2+4+6
%e 1+1+1+4+6 1+1+2+5+5
%e 1+1+1+5+5 1+1+3+3+6
%e 1+1+1+1+8 1+1+2+2+7 1+1+3+4+5
%e 1+1+1+2+7 1+1+2+3+6 1+1+4+4+4
%e 1+1+1+3+6 1+1+2+4+5 1+2+2+2+7
%e 1+1+1+1+7 1+1+1+4+5 1+1+3+3+5 1+2+2+3+6
%e 1+1+1+2+6 1+1+2+2+6 1+1+3+4+4 1+2+2+4+5
%e 1+1+1+3+5 1+1+2+3+5 1+2+2+2+6 1+2+3+3+5
%e 1+1+1+1+6 1+1+1+4+4 1+1+2+4+4 1+2+2+3+5 1+2+3+4+4
%e 1+1+1+2+5 1+1+2+2+5 1+1+3+3+4 1+2+2+4+4 1+3+3+3+4
%e 1+1+1+3+4 1+1+2+3+4 1+2+2+2+5 1+2+3+3+4 2+2+2+2+6
%e 1+1+2+2+4 1+1+3+3+3 1+2+2+3+4 1+3+3+3+3 2+2+2+3+5
%e 1+1+2+3+3 1+2+2+2+4 1+2+3+3+3 2+2+2+2+5 2+2+2+4+4
%e 1+2+2+2+3 1+2+2+3+3 2+2+2+2+4 2+2+2+3+4 2+2+3+3+4
%e 2+2+2+2+2 2+2+2+2+3 2+2+2+3+3 2+2+3+3+3 2+3+3+3+3
%e --------------------------------------------------------------------------
%e n | 10 11 12 13 14 ...
%e --------------------------------------------------------------------------
%e a(n) | 27 44 64 96 134 ...
%e --------------------------------------------------------------------------
%e - _Wesley Ivan Hurt_, Sep 12 2019
%t Table[Sum[Sum[Sum[Sum[n - i - j - k - l, {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 100}]
%Y Cf. A026811, A308822, A308823, A308824, A308825, A308826.
%K nonn
%O 0,7
%A _Wesley Ivan Hurt_, Jun 26 2019