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 A309834 #21 Nov 07 2019 08:13:22
%S A309834 0,0,0,0,0,0,0,0,0,0,2,2,4,6,10,12,18,22,30,36,50,58,76,90,114,132,
%T A309834 164,188,228,260,314,354,420,474,556,622,722,804,924,1024,1172,1292,
%U A309834 1466,1614,1820,1994,2236,2442,2722,2964,3294,3574,3952,4282,4716,5094
%N A309834 Sum of the even parts appearing among the smallest parts of the partitions of n into 5 parts.
%H A309834 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A309834 <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,-2,0,0,1,1,1,-2,-2,0,0,4,0,0,-2,-2,1,1,1,0,0,-2,0,0,1,1,-1).
%F A309834 a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-l)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} l * ((l-1) mod 2).
%F A309834 a(n) = a(n-1) + a(n-2) - 2*a(n-5) + a(n-8) + a(n-9) + a(n-10) - 2*a(n-11) - 2*a(n-12) + 4*a(n-15) - 2*a(n-18) - 2*a(n-19) + a(n-20) + a(n-21) + a(n-22) - 2*a(n-25) + a(n-28) + a(n-29) - a(n-30) for n > 29.
%e A309834 Figure 1: The partitions of n into 5 parts for n = 10, 11, ..
%e A309834 1+1+1+1+10
%e A309834 1+1+1+2+9
%e A309834 1+1+1+3+8
%e A309834 1+1+1+4+7
%e A309834 1+1+1+5+6
%e A309834 1+1+1+1+9 1+1+2+2+8
%e A309834 1+1+1+2+8 1+1+2+3+7
%e A309834 1+1+1+3+7 1+1+2+4+6
%e A309834 1+1+1+4+6 1+1+2+5+5
%e A309834 1+1+1+5+5 1+1+3+3+6
%e A309834 1+1+1+1+8 1+1+2+2+7 1+1+3+4+5
%e A309834 1+1+1+2+7 1+1+2+3+6 1+1+4+4+4
%e A309834 1+1+1+3+6 1+1+2+4+5 1+2+2+2+7
%e A309834 1+1+1+1+7 1+1+1+4+5 1+1+3+3+5 1+2+2+3+6
%e A309834 1+1+1+2+6 1+1+2+2+6 1+1+3+4+4 1+2+2+4+5
%e A309834 1+1+1+3+5 1+1+2+3+5 1+2+2+2+6 1+2+3+3+5
%e A309834 1+1+1+1+6 1+1+1+4+4 1+1+2+4+4 1+2+2+3+5 1+2+3+4+4
%e A309834 1+1+1+2+5 1+1+2+2+5 1+1+3+3+4 1+2+2+4+4 1+3+3+3+4
%e A309834 1+1+1+3+4 1+1+2+3+4 1+2+2+2+5 1+2+3+3+4 2+2+2+2+6
%e A309834 1+1+2+2+4 1+1+3+3+3 1+2+2+3+4 1+3+3+3+3 2+2+2+3+5
%e A309834 1+1+2+3+3 1+2+2+2+4 1+2+3+3+3 2+2+2+2+5 2+2+2+4+4
%e A309834 1+2+2+2+3 1+2+2+3+3 2+2+2+2+4 2+2+2+3+4 2+2+3+3+4
%e A309834 2+2+2+2+2 2+2+2+2+3 2+2+2+3+3 2+2+3+3+3 2+3+3+3+3
%e A309834 --------------------------------------------------------------------------
%e A309834 n | 10 11 12 13 14 ...
%e A309834 --------------------------------------------------------------------------
%e A309834 a(n) | 2 2 4 6 10 ...
%e A309834 --------------------------------------------------------------------------
%t A309834 LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, 1, -2, -2, 0, 0, 4, 0,
%t A309834 0, -2, -2, 1, 1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {0, 0, 0, 0, 0, 0, 0,
%t A309834 0, 0, 0, 2, 2, 4, 6, 10, 12, 18, 22, 30, 36, 50, 58, 76, 90, 114,
%t A309834 132, 164, 188, 228, 260}, 50]
%Y A309834 Cf. A309787, A309830, A309831.
%K A309834 nonn,easy
%O A309834 0,11
%A A309834 _Wesley Ivan Hurt_, Aug 19 2019