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 A308843 #20 Dec 26 2022 19:16:40
%S A308843 0,0,0,0,0,1,1,2,3,6,8,12,13,21,23,32,33,49,56,77,86,117,130,162,174,
%T A308843 223,239,295,312,391,418,497,520,631,675,801,844,1009,1072,1247,1306,
%U A308843 1537,1628,1890,1972,2312,2425,2786,2889,3325,3472,3955,4089,4671,4851,5474
%N A308843 Sum of the third largest parts in the partitions of n into 5 squarefree parts.
%C A308843 Conjecture: a(4*k + 3) < a(4*k + 4) for 4*k + 3 >= 195. This conjecture holds for all terms in the b-file. - _David A. Corneth_, Sep 16 2019
%H A308843 David A. Corneth, <a href="/A308843/b308843.txt">Table of n, a(n) for n = 0..1000</a>
%H A308843 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308843 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)} mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k-l)^2 * j, where mu is the Möbius function (A008683).
%F A308843 a(n) = A308839(n) - A308841(n) - A308842(n) - A308844(n) - A308845(n).
%t A308843 Table[Sum[Sum[Sum[Sum[j * MoebiusMu[l]^2*MoebiusMu[k]^2*MoebiusMu[j]^2 *MoebiusMu[i]^2*MoebiusMu[n - i - j - k - l]^2, {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, 50}]
%t A308843 Table[Total[Select[IntegerPartitions[n,{5}],AllTrue[#,SquareFreeQ]&][[All,3]]],{n,0,60}] (* _Harvey P. Dale_, Dec 26 2022 *)
%Y A308843 Cf. A008683, A308839, A308840, A308841, A308842, A308844, A308845.
%K A308843 nonn
%O A308843 0,8
%A A308843 _Wesley Ivan Hurt_, Jun 28 2019
%E A308843 a(54)..a(55) from _David A. Corneth_, Sep 16 2019