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 A189426 #17 Jun 02 2025 04:02:10
%S A189426 0,0,1,4,14,42,119,322,847,2180,5521,13804,34160,83818,204204,494494,
%T A189426 1191227,2856666,6823334,16240714,38534657,91175154,215179125,
%U A189426 506670394,1190534467,2792076392,6536567296,15278103876,35656587624,83101366684
%N A189426 Expansion of (x^2)/(1-2*x-x^2+x^3)^2.
%C A189426 Convolution of A006054={0,0,1,2,5,11,25,56,126,...} with itself.
%C A189426 For n=0,1,2,..., partial sums are given by Sum_{k=0..n} a(k)=A189427(n), where A189427={0,0,1,5,19,61,180,...}.
%H A189426 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4, -2, -6, 3, 2, -1).
%F A189426 G.f.: (x^2)/(1-2*x-x^2+x^3)^2.
%F A189426 a(n)=4*a(n-1)-2*a(n-2)-6*a(n-3)+3*a(n-4)+2*a(n-5)-a(n-6), n>=6.
%t A189426 CoefficientList[Series[x^2/(1-2x-x^2+x^3)^2,{x,0,40}],x] (* or *) LinearRecurrence[{4,-2,-6,3,2,-1},{0,0,1,4,14,42},40] (* _Harvey P. Dale_, Feb 29 2012 *)
%o A189426 (PARI) Vec((x^2)/(1-2*x-x^2+x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y A189426 Cf. A006054, A189427.
%K A189426 nonn,easy
%O A189426 0,4
%A A189426 _L. Edson Jeffery_, Apr 22 2011