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 A308759 #23 Sep 12 2021 22:02:12
%S A308759 0,0,0,0,1,1,3,5,10,13,23,30,46,59,83,103,141,170,220,265,334,392,484,
%T A308759 563,680,784,930,1061,1247,1409,1631,1836,2106,2349,2673,2967,3348,
%U A308759 3699,4143,4554,5077,5554,6150,6710,7396,8032,8816,9546,10432,11264,12260
%N A308759 Sum of the second largest parts of the partitions of n into 4 parts.
%H A308759 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308759 a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} i.
%F A308759 a(n) = A308775(n) - A308733(n) - A308758(n) - A308760(n).
%F A308759 Conjectures from _Colin Barker_, Jun 23 2019: (Start)
%F A308759 G.f.: x^4*(1 + x + 2*x^2 + 2*x^3 + 3*x^4 + 2*x^5 + 2*x^6) / ((1 - x)^5*(1 + x)^3*(1 + x^2)^2*(1 + x + x^2)^2).
%F A308759 a(n) = a(n-2) + 2*a(n-3) + 2*a(n-4) - 2*a(n-5) - 3*a(n-6) - 4*a(n-7) + 4*a(n-9) + 3*a(n-10) + 2*a(n-11) - 2*a(n-12) - 2*a(n-13) - a(n-14) + a(n-16) for n>15.
%F A308759 (End)
%e A308759 Figure 1: The partitions of n into 4 parts for n = 8, 9, ..
%e A308759 1+1+1+9
%e A308759 1+1+2+8
%e A308759 1+1+3+7
%e A308759 1+1+4+6
%e A308759 1+1+1+8 1+1+5+5
%e A308759 1+1+2+7 1+2+2+7
%e A308759 1+1+1+7 1+1+3+6 1+2+3+6
%e A308759 1+1+2+6 1+1+4+5 1+2+4+5
%e A308759 1+1+3+5 1+2+2+6 1+3+3+5
%e A308759 1+1+1+6 1+1+4+4 1+2+3+5 1+3+4+4
%e A308759 1+1+1+5 1+1+2+5 1+2+2+5 1+2+4+4 2+2+2+6
%e A308759 1+1+2+4 1+1+3+4 1+2+3+4 1+3+3+4 2+2+3+5
%e A308759 1+1+3+3 1+2+2+4 1+3+3+3 2+2+2+5 2+2+4+4
%e A308759 1+2+2+3 1+2+3+3 2+2+2+4 2+2+3+4 2+3+3+4
%e A308759 2+2+2+2 2+2+2+3 2+2+3+3 2+3+3+3 3+3+3+3
%e A308759 --------------------------------------------------------------------------
%e A308759 n | 8 9 10 11 12 ...
%e A308759 --------------------------------------------------------------------------
%e A308759 a(n) | 10 13 23 30 46 ...
%e A308759 --------------------------------------------------------------------------
%e A308759 - _Wesley Ivan Hurt_, Sep 07 2019
%t A308759 Table[Total[IntegerPartitions[n,{4}][[All,2]]],{n,0,50}] (* _Harvey P. Dale_, Nov 08 2020 *)
%Y A308759 Cf. A026810, A308733, A308758, A308760, A308775.
%K A308759 nonn
%O A308759 0,7
%A A308759 _Wesley Ivan Hurt_, Jun 22 2019