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 A171218 #25 Mar 20 2023 03:37:13
%S A171218 0,2,6,16,32,58,94,144,208,290,390,512,656,826,1022,1248,1504,1794,
%T A171218 2118,2480,2880,3322,3806,4336,4912,5538,6214,6944,7728,8570,9470,
%U A171218 10432,11456,12546,13702,14928,16224,17594,19038,20560,22160,23842,25606
%N A171218 a(n) = Sum_{k=0..n} A109613(k)*A005843(n-k).
%C A171218 a(n) is the number of triples (w,x,y) with all terms in {0,...,n} and 2|w-x|<max(w,x,y)-min(w,x,y). [_Clark Kimberling_, Jun 11 2012]
%H A171218 Vincenzo Librandi, <a href="/A171218/b171218.txt">Table of n, a(n) for n = 0..10000</a>
%H A171218 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A171218 a(n+1) - a(n) = A137928(n+1).
%F A171218 From _Bruno Berselli_, Nov 16 2011: (Start)
%F A171218 G.f.: 2*x*(1+x^2)/((1+x)*(1-x)^4).
%F A171218 a(n) = 2*A131941(n) = (2*n*(2*n^2+3*n+4)-3*(-1)^n+3)/12.
%F A171218 a(n) = -a(-n-1) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5). (End)
%t A171218 CoefficientList[Series[2x (1+x^2)/((1+x)(1-x)^4),{x,0,50}],x] (* or *) LinearRecurrence[ {3,-2,-2,3,-1},{0,2,6,16,32},50] (* _Harvey P. Dale_, Jan 22 2023 *)
%o A171218 (Magma) [&+[(2*k+(-1)^k+1)*(n-k): k in [0..n]]: n in [0..42]]; // _Bruno Berselli_, Nov 16 2011
%K A171218 nonn,easy
%O A171218 0,2
%A A171218 _Reinhard Zumkeller_, Dec 05 2009