This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A308825 #12 Oct 01 2024 18:40:44
%S A308825 0,0,0,0,0,1,1,2,4,7,11,17,24,36,50,69,91,123,158,204,259,326,403,499,
%T A308825 606,739,886,1060,1256,1489,1745,2041,2371,2750,3166,3643,4160,4750,
%U A308825 5393,6112,6897,7774,8720,9772,10910,12168,13518,15006,16601,18352,20229
%N A308825 Sum of the third largest parts of the partitions of n into 5 parts.
%H A308825 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308825 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)} j.
%F A308825 a(n) = A308822(n) - A308823(n) - A308824(n) - A308826(n) - A308827(n).
%e A308825 The partitions of n into 5 parts for n = 10, 11, ..
%e A308825 1+1+1+1+10
%e A308825 1+1+1+2+9
%e A308825 1+1+1+3+8
%e A308825 1+1+1+4+7
%e A308825 1+1+1+5+6
%e A308825 1+1+1+1+9 1+1+2+2+8
%e A308825 1+1+1+2+8 1+1+2+3+7
%e A308825 1+1+1+3+7 1+1+2+4+6
%e A308825 1+1+1+4+6 1+1+2+5+5
%e A308825 1+1+1+5+5 1+1+3+3+6
%e A308825 1+1+1+1+8 1+1+2+2+7 1+1+3+4+5
%e A308825 1+1+1+2+7 1+1+2+3+6 1+1+4+4+4
%e A308825 1+1+1+3+6 1+1+2+4+5 1+2+2+2+7
%e A308825 1+1+1+1+7 1+1+1+4+5 1+1+3+3+5 1+2+2+3+6
%e A308825 1+1+1+2+6 1+1+2+2+6 1+1+3+4+4 1+2+2+4+5
%e A308825 1+1+1+3+5 1+1+2+3+5 1+2+2+2+6 1+2+3+3+5
%e A308825 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 A308825 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 A308825 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 A308825 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 A308825 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 A308825 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 A308825 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 A308825 --------------------------------------------------------------------------
%e A308825 n | 10 11 12 13 14 ...
%e A308825 --------------------------------------------------------------------------
%e A308825 a(n) | 11 17 24 36 50 ...
%e A308825 --------------------------------------------------------------------------
%e A308825 - _Wesley Ivan Hurt_, Sep 11 2019
%t A308825 Table[Sum[Sum[Sum[Sum[j, {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}]
%t A308825 Table[Total[IntegerPartitions[n,{5}][[;;,3]]],{n,0,50}] (* _Harvey P. Dale_, Oct 01 2024 *)
%Y A308825 Cf. A026811, A308822, A308823, A308824, A308826, A308827.
%K A308825 nonn
%O A308825 0,8
%A A308825 _Wesley Ivan Hurt_, Jun 26 2019