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 A105371 #22 May 08 2024 05:44:30
%S A105371 1,1,1,0,-3,-8,-13,-13,0,34,89,144,144,0,-377,-987,-1597,-1597,0,4181,
%T A105371 10946,17711,17711,0,-46368,-121393,-196418,-196418,0,514229,1346269,
%U A105371 2178309,2178309,0,-5702887,-14930352,-24157817,-24157817,0,63245986,165580141
%N A105371 Expansion of (1-x)*(1-x+x^2)/(1-3*x+4*x^2-2*x^3+x^4).
%C A105371 Binomial transform of A105367.
%H A105371 <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%H A105371 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-4,2,-1).
%F A105371 G.f.: (1-2x+2x^2-x^3)/(1-3x+4x^2-2x^3+x^4).
%F A105371 a(n) = 3*a(n-1)-4*a(n-2)+2*a(n-3)-a(n-4).
%F A105371 a(n) = (1/2+sqrt(5)/2)^n((1/2+sqrt(5)/10)cos(Pi*n/5)+sqrt(1/10-sqrt(5)/50)sin(Pi*n/5))- (sqrt(5)/2-1/2)^n((sqrt(5)/10-1/2)cos(2*Pi*n/5)+sqrt(1/10+sqrt(5)/50)sin(2*Pi*n/5)).
%F A105371 a(5n) = -F(-5n-1), a(5n+1) = a(5n+2) = -F(-5n-2), a(5n+3) = 0, a(5n+4) = F(-5n-4). - _Michael Somos_, Apr 09 2005
%t A105371 CoefficientList[Series[(1-x)(1-x+x^2)/(1-3x+4x^2-2x^3+x^4),{x,0,60}],x] (* or *) LinearRecurrence[{3,-4,2,-1},{1,1,1,0},60] (* _Harvey P. Dale_, Dec 21 2013 *)
%o A105371 (PARI) a(n)=local(m); m=n%5+1; [1,-1,-1,0,1][m]*fibonacci(-n-(m<3)) /* _Michael Somos_, Apr 09 2005 */
%Y A105371 Cf. A000045, A105367.
%K A105371 easy,sign
%O A105371 0,5
%A A105371 _Paul Barry_, Apr 01 2005