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 A309793 #24 Nov 07 2019 07:02:01
%S A309793 0,0,0,0,1,1,1,1,2,3,5,6,8,9,11,13,17,20,24,27,32,36,42,47,54,60,68,
%T A309793 75,85,93,103,112,124,135,149,161,176,189,205,220,239,256,276,294,316,
%U A309793 336,360,382,408,432,460,486,517,545,577,607,642,675,713,748
%N A309793 Number of odd parts appearing among the second largest parts of the partitions of n into 4 parts.
%H A309793 Colin Barker, <a href="/A309793/b309793.txt">Table of n, a(n) for n = 0..1000</a>
%H A309793 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A309793 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,1,-2,2,-2,1,0,0,0,-1,2,-1).
%F A309793 a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} (i mod 2).
%F A309793 From _Colin Barker_, Aug 18 2019: (Start)
%F A309793 G.f.: x^4*(1 - x + x^4) / ((1 - x)^4*(1 + x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 + x^4)).
%F A309793 a(n) = 2*a(n-1) - a(n-2) + a(n-6) - 2*a(n-7) + 2*a(n-8) - 2*a(n-9) + a(n-10) - a(n-14) + 2*a(n-15) - a(n-16) for n>15.
%F A309793 (End) [Recurrence verified by _Wesley Ivan Hurt_, Aug 24 2019]
%e A309793 Figure 1: The partitions of n into 4 parts for n = 8, 9, ..
%e A309793 1+1+1+9
%e A309793 1+1+2+8
%e A309793 1+1+3+7
%e A309793 1+1+4+6
%e A309793 1+1+1+8 1+1+5+5
%e A309793 1+1+2+7 1+2+2+7
%e A309793 1+1+1+7 1+1+3+6 1+2+3+6
%e A309793 1+1+2+6 1+1+4+5 1+2+4+5
%e A309793 1+1+3+5 1+2+2+6 1+3+3+5
%e A309793 1+1+1+6 1+1+4+4 1+2+3+5 1+3+4+4
%e A309793 1+1+1+5 1+1+2+5 1+2+2+5 1+2+4+4 2+2+2+6
%e A309793 1+1+2+4 1+1+3+4 1+2+3+4 1+3+3+4 2+2+3+5
%e A309793 1+1+3+3 1+2+2+4 1+3+3+3 2+2+2+5 2+2+4+4
%e A309793 1+2+2+3 1+2+3+3 2+2+2+4 2+2+3+4 2+3+3+4
%e A309793 2+2+2+2 2+2+2+3 2+2+3+3 2+3+3+3 3+3+3+3
%e A309793 --------------------------------------------------------------------------
%e A309793 n | 8 9 10 11 12 ...
%e A309793 --------------------------------------------------------------------------
%e A309793 a(n) | 2 3 5 6 8 ...
%e A309793 --------------------------------------------------------------------------
%t A309793 LinearRecurrence[{2, -1, 0, 0, 0, 1, -2, 2, -2, 1, 0, 0, 0, -1, 2, -1}, {0, 0, 0, 0, 1, 1, 1, 1, 2, 3, 5, 6, 8, 9, 11, 13}, 50]
%o A309793 (PARI) concat([0,0,0,0], Vec(x^4*(1 - x + x^4) / ((1 - x)^4*(1 + x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 + x^4)) + O(x^50))) \\ _Colin Barker_, Oct 10 2019
%Y A309793 Cf. A309795, A309797, A026928.
%K A309793 nonn,easy
%O A309793 0,9
%A A309793 _Wesley Ivan Hurt_, Aug 17 2019