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 A309795 #21 Oct 10 2019 08:16:30
%S A309795 0,0,0,0,0,0,1,2,3,3,4,5,7,9,12,14,17,19,23,27,32,36,42,47,54,60,68,
%T A309795 75,84,92,103,113,125,135,148,160,175,189,206,221,239,255,275,294,316,
%U A309795 336,360,382,408,432,460,486,516,544,577,608,643,675,712,747
%N A309795 Number of even parts appearing among the second largest parts of the partitions of n into 4 parts.
%H A309795 Colin Barker, <a href="/A309795/b309795.txt">Table of n, a(n) for n = 0..1000</a>
%H A309795 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A309795 <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 A309795 a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} ((i-1) mod 2).
%F A309795 From _Colin Barker_, Aug 18 2019: (Start)
%F A309795 G.f.: x^6*(1 - x^3 + x^4) / ((1 - x)^4*(1 + x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 + x^4)).
%F A309795 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 A309795 (End) [Recurrence verified by _Wesley Ivan Hurt_, Aug 25 2019]
%e A309795 Figure 1: The partitions of n into 4 parts for n = 8, 9, ..
%e A309795 1+1+1+9
%e A309795 1+1+2+8
%e A309795 1+1+3+7
%e A309795 1+1+4+6
%e A309795 1+1+1+8 1+1+5+5
%e A309795 1+1+2+7 1+2+2+7
%e A309795 1+1+1+7 1+1+3+6 1+2+3+6
%e A309795 1+1+2+6 1+1+4+5 1+2+4+5
%e A309795 1+1+3+5 1+2+2+6 1+3+3+5
%e A309795 1+1+1+6 1+1+4+4 1+2+3+5 1+3+4+4
%e A309795 1+1+1+5 1+1+2+5 1+2+2+5 1+2+4+4 2+2+2+6
%e A309795 1+1+2+4 1+1+3+4 1+2+3+4 1+3+3+4 2+2+3+5
%e A309795 1+1+3+3 1+2+2+4 1+3+3+3 2+2+2+5 2+2+4+4
%e A309795 1+2+2+3 1+2+3+3 2+2+2+4 2+2+3+4 2+3+3+4
%e A309795 2+2+2+2 2+2+2+3 2+2+3+3 2+3+3+3 3+3+3+3
%e A309795 --------------------------------------------------------------------------
%e A309795 n | 8 9 10 11 12 ...
%e A309795 --------------------------------------------------------------------------
%e A309795 a(n) | 3 3 4 5 7 ...
%e A309795 --------------------------------------------------------------------------
%t A309795 LinearRecurrence[{2, -1, 0, 0, 0, 1, -2, 2, -2, 1, 0, 0, 0, -1, 2, -1}, {0, 0, 0, 0, 0, 0, 1, 2, 3, 3, 4, 5, 7, 9, 12, 14}, 50]
%o A309795 (PARI) concat([0,0,0,0,0,0], Vec(x^6*(1 - x^3 + x^4) / ((1 - x)^4*(1 + x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 + x^4)) + O(x^70))) \\ _Colin Barker_, Oct 10 2019
%Y A309795 Cf. A309793, A309797, A026928.
%K A309795 nonn,easy
%O A309795 0,8
%A A309795 _Wesley Ivan Hurt_, Aug 17 2019