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%I #18 Apr 10 2022 14:40:07
%S 1,1,1,0,-3,-8,-13,-13,0,34,89,144,144,0,-377,-987,-1597,-1597,0,4181,
%T 10946,17711,17711,0,-46368,-121393,-196418,-196418,0,514229,1346269,
%U 2178309,2178309,0,-5702887,-14930352,-24157817,-24157817,0,63245986,165580141
%N Expansion of (1-x)(1-x+x^2)/(1-3x+4x^2-2x^3+x^4).
%C Binomial transform of A105367.
%H <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,-4,2,-1)
%F G.f.: (1-2x+2x^2-x^3)/(1-3x+4x^2-2x^3+x^4); a(n)=3*a(n-1)-4*a(n-2)+2*a(n-3)-a(n-4); (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 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 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 (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 Cf. A000045, A105367.
%K easy,sign
%O 0,5
%A _Paul Barry_, Apr 01 2005
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