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 A308824 #15 Sep 09 2019 01:42:14
%S A308824 0,0,0,0,0,1,1,2,3,6,9,13,18,27,36,50,64,86,109,140,175,220,269,331,
%T A308824 399,486,577,689,811,959,1119,1305,1508,1747,2003,2300,2617,2984,3376,
%U A308824 3821,4300,4839,5415,6060,6749,7521,8337,9243,10207,11273,12404,13641
%N A308824 Sum of the fourth largest parts in the partitions of n into 5 parts.
%H A308824 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308824 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)} k.
%F A308824 a(n) = A308822(n) - A308823(n) - A308825(n) - A308826(n) - A308827(n).
%F A308824 Conjectures from _Colin Barker_, Jun 30 2019: (Start)
%F A308824 G.f.: x^5*(1 + x^3 + x^6) / ((1 - x)^6*(1 + x)^3*(1 + x^2)^2*(1 + x + x^2 + x^3 + x^4)^2).
%F A308824 a(n) = a(n-1) + a(n-2) - a(n-3) + 2*a(n-4) - 4*a(n-6) + a(n-8) - 3*a(n-9) + 4*a(n-10) + 4*a(n-11) - 3*a(n-12) + a(n-13) - 4*a(n-15) + 2*a(n-17) - a(n-18) + a(n-19) + a(n-20) - a(n-21) for n>20.
%F A308824 (End)
%e A308824 The partitions of n into 5 parts for n = 10, 11, ..
%e A308824 1+1+1+1+10
%e A308824 1+1+1+2+9
%e A308824 1+1+1+3+8
%e A308824 1+1+1+4+7
%e A308824 1+1+1+5+6
%e A308824 1+1+1+1+9 1+1+2+2+8
%e A308824 1+1+1+2+8 1+1+2+3+7
%e A308824 1+1+1+3+7 1+1+2+4+6
%e A308824 1+1+1+4+6 1+1+2+5+5
%e A308824 1+1+1+5+5 1+1+3+3+6
%e A308824 1+1+1+1+8 1+1+2+2+7 1+1+3+4+5
%e A308824 1+1+1+2+7 1+1+2+3+6 1+1+4+4+4
%e A308824 1+1+1+3+6 1+1+2+4+5 1+2+2+2+7
%e A308824 1+1+1+1+7 1+1+1+4+5 1+1+3+3+5 1+2+2+3+6
%e A308824 1+1+1+2+6 1+1+2+2+6 1+1+3+4+4 1+2+2+4+5
%e A308824 1+1+1+3+5 1+1+2+3+5 1+2+2+2+6 1+2+3+3+5
%e A308824 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 A308824 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 A308824 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 A308824 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 A308824 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 A308824 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 A308824 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 A308824 --------------------------------------------------------------------------
%e A308824 n | 10 11 12 13 14 ...
%e A308824 --------------------------------------------------------------------------
%e A308824 a(n) | 9 13 18 27 36 ...
%e A308824 --------------------------------------------------------------------------
%e A308824 - _Wesley Ivan Hurt_, Sep 08 2019
%t A308824 Table[Sum[Sum[Sum[Sum[k, {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 A308824 Cf. A026811, A308822, A308823, A308825, A308826, A308827.
%K A308824 nonn
%O A308824 0,8
%A A308824 _Wesley Ivan Hurt_, Jun 26 2019