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 A204467 #21 Oct 31 2018 17:04:33
%S A204467 1,8,25,50,85,128,181,242,313,392,481,578,685,800,925,1058,1201,1352,
%T A204467 1513,1682,1861,2048,2245,2450,2665,2888,3121,3362,3613,3872,4141,
%U A204467 4418,4705,5000,5305,5618,5941,6272,6613,6962,7321,7688,8065,8450,8845,9248,9661
%N A204467 Number of 3-element subsets that can be chosen from {1,2,...,6*n+3} having element sum 9*n+6.
%C A204467 a(n) is the number of partitions of 9*n+6 into 3 distinct parts <= 6*n+3.
%H A204467 Alois P. Heinz, <a href="/A204467/b204467.txt">Table of n, a(n) for n = 0..1000</a>
%H A204467 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, -2, 1).
%F A204467 a(n) = 1+floor((3+9/2*n)*n).
%F A204467 G.f.: -(2*x+1)*(x^2+4*x+1)/((x+1)*(x-1)^3).
%F A204467 a(n) = (6*n*(3*n+2)+(-1)^n+3)/4. - _Bruno Berselli_, Jan 17 2012
%F A204467 a(0)=1, a(1)=8, a(2)=25, a(3)=50, a(n)=2*a(n-1)-2*a(n-3)+a(n-4). - _Harvey P. Dale_, May 25 2015
%e A204467 a(1) = 8 because there are 8 3-element subsets that can be chosen from {1,2,...,9} having element sum 15: {1,5,9}, {1,6,8}, {2,4,9}, {2,5,8}, {2,6,7}, {3,4,8}, {3,5,7}, {4,5,6}.
%p A204467 a:= n-> 1 +floor((3+9/2*n)*n):
%p A204467 seq(a(n), n=0..50);
%t A204467 Table[(6n(3n+2)+(-1)^n+3)/4,{n,0,50}] (* or *) LinearRecurrence[{2,0,-2,1},{1,8,25,50},50] (* _Harvey P. Dale_, May 25 2015 *)
%Y A204467 Bisection of column k=3 of A204459.
%Y A204467 Cf. A104185.
%K A204467 nonn,easy
%O A204467 0,2
%A A204467 _Alois P. Heinz_, Jan 16 2012