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 A102517 #14 Aug 29 2025 10:13:38
%S A102517 1,1,-1,-2,1,3,-2,-5,5,10,-11,-21,22,43,-43,-86,85,171,-170,-341,341,
%T A102517 682,-683,-1365,1366,2731,-2731,-5462,5461,10923,-10922,-21845,21845,
%U A102517 43690,-43691,-87381,87382,174763,-174763,-349526,349525,699051,-699050,-1398101,1398101,2796202,-2796203,-5592405
%N A102517 Expansion of (1+x^2)/((1-x+x^2)*(1+2*x^2)).
%H A102517 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,-3,2,-2).
%F A102517 G.f.: (1+x^2)^2/((1+x^2)^3+x^6)+x(1+x^2)/((1+x^2)^3+x^6).
%F A102517 a(n) = Sum_{k=0..floor(n/2)} T(n-k, k)*(-1)^k, T(n, k) = Sum_{i=0..k} C(n, i) (A008949).
%F A102517 a(n) = (-1)^(n/2)*(Sum_{k=0..floor(n/6)} C(n/2, 3*k))*(1+(-1)^n)/2 + (-1)^((n-1)/2)*(Sum_{k=0..floor((n+1)/6)} C((n+1)/2, 3*k+1))*(1-(-1)^n)/2.
%F A102517 a(n) = 2^(n/2)*(cos(Pi*n/2)/3+sqrt(2)*sin(Pi*n/2)/3)+cos(Pi*n/3+Pi/3)/3+sqrt(3)*sin(Pi*n/3+Pi/3)/3.
%F A102517 a(2*n) = (-1)^n*A024493(n); a(2*n+1) = (-1)^n*A024494(n).
%F A102517 a(0)=1, a(1)=1, a(2)=-1, a(3)=-2, a(n) = a(n-1)-3*a(n-2)+2*a(n-3)-2*a(n-4). - _Harvey P. Dale_, Oct 28 2011
%t A102517 CoefficientList[Series[(1+x^2)/((1-x+x^2)(1+2x^2)),{x,0,50}],x] (* or *) LinearRecurrence[{1,-3,2,-2},{1,1,-1,-2},50] (* _Harvey P. Dale_, Oct 28 2011 *)
%Y A102517 Cf. A001045, A078008.
%K A102517 easy,sign,changed
%O A102517 0,4
%A A102517 _Paul Barry_, Jan 13 2005