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 A204468 #22 Feb 25 2021 12:00:11
%S A204468 0,1,8,33,86,177,318,519,790,1143,1588,2135,2796,3581,4500,5565,6786,
%T A204468 8173,9738,11491,13442,15603,17984,20595,23448,26553,29920,33561,
%U A204468 37486,41705,46230,51071,56238,61743,67596,73807,80388,87349,94700,102453,110618,119205
%N A204468 Number of 4-element subsets that can be chosen from {1,2,...,4*n} having element sum 8*n+2.
%C A204468 a(n) is the number of partitions of 8*n+2 into 4 distinct parts <= 4*n.
%H A204468 Alois P. Heinz, <a href="/A204468/b204468.txt">Table of n, a(n) for n = 0..1000</a>
%H A204468 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 2, -3, 3, -1).
%F A204468 G.f.: x*(5*x^4+9*x^3+12*x^2+5*x+1)/((x^2+x+1)*(x-1)^4).
%F A204468 a(n) = (1/9)*(2*A102283(n) + n*(16*n^2-18*n+9)). - _Bruno Berselli_, Jan 19 2012
%e A204468 a(2) = 8 because there are 8 4-element subsets that can be chosen from {1,2,...,8} having element sum 18: {1,2,7,8}, {1,3,6,8}, {1,4,5,8}, {1,4,6,7}, {2,3,5,8}, {2,3,6,7}, {2,4,5,7}, {3,4,5,6}.
%p A204468 a:= n-> ((9+(16*n-18)*n)*n +[0, 2, -2][irem(n, 3)+1])/9:
%p A204468 seq(a(n), n=0..50);
%t A204468 LinearRecurrence[{3,-3,2,-3,3,-1},{0,1,8,33,86,177},50] (* or *) CoefficientList[Series[(x (1+5 x+12 x^2+9 x^3+5 x^4))/((-1+x)^4 (1+x+x^2)),{x,0,50}],x] (* _Harvey P. Dale_, Feb 25 2021 *)
%Y A204468 Column k=4 of A204459.
%K A204468 nonn,easy
%O A204468 0,3
%A A204468 _Alois P. Heinz_, Jan 16 2012