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 A308760 #21 Sep 07 2019 09:47:16
%S A308760 0,0,0,0,1,2,5,9,17,25,41,57,84,112,154,197,262,325,414,506,629,751,
%T A308760 915,1078,1289,1501,1767,2034,2370,2701,3108,3519,4014,4506,5100,5691,
%U A308760 6393,7095,7917,8739,9703,10658,11765,12876,14150,15418,16874,18324,19974
%N A308760 Sum of the largest parts of the partitions of n into 4 parts.
%H A308760 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308760 a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} (n-i-j-k).
%F A308760 a(n) = A308775(n) - A308733(n) - A308758(n) - A308759(n).
%F A308760 Conjectures from _Colin Barker_, Jun 23 2019: (Start)
%F A308760 G.f.: x^4*(1 + 2*x + 4*x^2 + 5*x^3 + 6*x^4 + 4*x^5 + 3*x^6) / ((1 - x)^5*(1 + x)^3*(1 + x^2)^2*(1 + x + x^2)^2).
%F A308760 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 A308760 (End)
%e A308760 Figure 1: The partitions of n into 4 parts for n = 8, 9, ..
%e A308760 1+1+1+9
%e A308760 1+1+2+8
%e A308760 1+1+3+7
%e A308760 1+1+4+6
%e A308760 1+1+1+8 1+1+5+5
%e A308760 1+1+2+7 1+2+2+7
%e A308760 1+1+1+7 1+1+3+6 1+2+3+6
%e A308760 1+1+2+6 1+1+4+5 1+2+4+5
%e A308760 1+1+3+5 1+2+2+6 1+3+3+5
%e A308760 1+1+1+6 1+1+4+4 1+2+3+5 1+3+4+4
%e A308760 1+1+1+5 1+1+2+5 1+2+2+5 1+2+4+4 2+2+2+6
%e A308760 1+1+2+4 1+1+3+4 1+2+3+4 1+3+3+4 2+2+3+5
%e A308760 1+1+3+3 1+2+2+4 1+3+3+3 2+2+2+5 2+2+4+4
%e A308760 1+2+2+3 1+2+3+3 2+2+2+4 2+2+3+4 2+3+3+4
%e A308760 2+2+2+2 2+2+2+3 2+2+3+3 2+3+3+3 3+3+3+3
%e A308760 --------------------------------------------------------------------------
%e A308760 n | 8 9 10 11 12 ...
%e A308760 --------------------------------------------------------------------------
%e A308760 a(n) | 17 25 41 57 84 ...
%e A308760 --------------------------------------------------------------------------
%e A308760 - _Wesley Ivan Hurt_, Sep 07 2019
%t A308760 Table[Sum[Sum[Sum[n - i - j - k, {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]
%Y A308760 Cf. A001318, A026810, A308265, A308733, A308758, A308759, A308775.
%K A308760 nonn
%O A308760 0,6
%A A308760 _Wesley Ivan Hurt_, Jun 22 2019