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 A308733 #37 Sep 07 2019 08:45:37
%S A308733 0,0,0,0,1,1,2,3,6,7,11,14,21,25,34,41,55,64,81,95,119,136,165,189,
%T A308733 227,256,301,339,396,441,507,564,645,711,804,885,996,1089,1215,1326,
%U A308733 1474,1600,1766,1914,2106,2272,2486,2678,2922,3136,3406,3650,3955,4225,4560
%N A308733 Sum of the smallest parts of the partitions of n into 4 parts.
%H A308733 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308733 a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} k.
%F A308733 a(n) = A308775(n) - A308758(n) - A308759(n) - A308760(n).
%F A308733 Conjectures from _Colin Barker_, Jun 23 2019: (Start)
%F A308733 G.f.: x^4 / ((1 - x)^5*(1 + x)^3*(1 + x^2)^2*(1 + x + x^2)).
%F A308733 a(n) = a(n-1) + a(n-2) + a(n-4) - 3*a(n-5) - a(n-6) + a(n-8) + 3*a(n-9) - a(n-10) - a(n-12) - a(n-13) + a(n-14) for n>13.
%F A308733 (End)
%e A308733 Figure 1: The partitions of n into 4 parts for n = 8, 9, ..
%e A308733 1+1+1+9
%e A308733 1+1+2+8
%e A308733 1+1+3+7
%e A308733 1+1+4+6
%e A308733 1+1+1+8 1+1+5+5
%e A308733 1+1+2+7 1+2+2+7
%e A308733 1+1+1+7 1+1+3+6 1+2+3+6
%e A308733 1+1+2+6 1+1+4+5 1+2+4+5
%e A308733 1+1+3+5 1+2+2+6 1+3+3+5
%e A308733 1+1+1+6 1+1+4+4 1+2+3+5 1+3+4+4
%e A308733 1+1+1+5 1+1+2+5 1+2+2+5 1+2+4+4 2+2+2+6
%e A308733 1+1+2+4 1+1+3+4 1+2+3+4 1+3+3+4 2+2+3+5
%e A308733 1+1+3+3 1+2+2+4 1+3+3+3 2+2+2+5 2+2+4+4
%e A308733 1+2+2+3 1+2+3+3 2+2+2+4 2+2+3+4 2+3+3+4
%e A308733 2+2+2+2 2+2+2+3 2+2+3+3 2+3+3+3 3+3+3+3
%e A308733 --------------------------------------------------------------------------
%e A308733 n | 8 9 10 11 12 ...
%e A308733 --------------------------------------------------------------------------
%e A308733 a(n) | 6 7 11 14 21 ...
%e A308733 --------------------------------------------------------------------------
%e A308733 - _Wesley Ivan Hurt_, Sep 07 2019
%t A308733 Table[Sum[Sum[Sum[k, {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]
%Y A308733 Cf. A026810, A308758, A308759, A308760, A308775.
%K A308733 nonn
%O A308733 0,7
%A A308733 _Wesley Ivan Hurt_, Jun 22 2019