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 A309543 #14 Sep 13 2019 22:36:29
%S A309543 0,0,0,0,0,5,4,8,10,17,20,32,38,56,66,90,104,137,158,200,230,285,324,
%T A309543 393,444,530,594,697,778,905,1004,1153,1274,1450,1594,1802,1972,2213,
%U A309543 2414,2690,2924,3242,3512,3873,4184,4595,4948,5410,5812,6330,6784,7362
%N A309543 Number of odd parts in the partitions of n into 5 parts.
%H A309543 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A309543 a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-1)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} ((i mod 2) + (j mod 2) + (k mod 2) + (l mod 2) + ((n-i-j-k-l) mod 2)).
%F A309543 G.f.: -x^5*(2*x^11-x^10+2*x^8+4*x^6-4*x^5+5*x^4-2*x^3+5*x^2-6*x+5) / ((x^2+1) *(x^2+x+1) *(x^2-x+1) *(x^4+x^3+x^2+x+1) *(x^4-x^3+x^2-x+1) *(x^4+1) *(x+1)^3 *(x-1)^5). - _Alois P. Heinz_, Aug 07 2019
%e A309543 The partitions of n into 5 parts for n = 10, 11, ..
%e A309543 1+1+1+1+10
%e A309543 1+1+1+2+9
%e A309543 1+1+1+3+8
%e A309543 1+1+1+4+7
%e A309543 1+1+1+5+6
%e A309543 1+1+1+1+9 1+1+2+2+8
%e A309543 1+1+1+2+8 1+1+2+3+7
%e A309543 1+1+1+3+7 1+1+2+4+6
%e A309543 1+1+1+4+6 1+1+2+5+5
%e A309543 1+1+1+5+5 1+1+3+3+6
%e A309543 1+1+1+1+8 1+1+2+2+7 1+1+3+4+5
%e A309543 1+1+1+2+7 1+1+2+3+6 1+1+4+4+4
%e A309543 1+1+1+3+6 1+1+2+4+5 1+2+2+2+7
%e A309543 1+1+1+1+7 1+1+1+4+5 1+1+3+3+5 1+2+2+3+6
%e A309543 1+1+1+2+6 1+1+2+2+6 1+1+3+4+4 1+2+2+4+5
%e A309543 1+1+1+3+5 1+1+2+3+5 1+2+2+2+6 1+2+3+3+5
%e A309543 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 A309543 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 A309543 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 A309543 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 A309543 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 A309543 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 A309543 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 A309543 --------------------------------------------------------------------------
%e A309543 n | 10 11 12 13 14 ...
%e A309543 --------------------------------------------------------------------------
%e A309543 a(n) | 20 32 38 56 66 ...
%e A309543 --------------------------------------------------------------------------
%e A309543 - _Wesley Ivan Hurt_, Sep 12 2019
%t A309543 Table[Sum[Sum[Sum[Sum[Mod[i, 2] + Mod[j, 2] + Mod[k, 2] + Mod[l, 2] + Mod[n - i - j - k - l, 2], {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 50}]
%Y A309543 Cf. A309516.
%K A309543 nonn,easy
%O A309543 0,6
%A A309543 _Wesley Ivan Hurt_, Aug 06 2019