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%I #21 Apr 19 2023 02:10:05
%S 0,1,2,0,-5,-5,8,21,0,-55,-55,89,233,0,-610,-610,987,2584,0,-6765,
%T -6765,10946,28657,0,-75025,-75025,121393,317811,0,-832040,-832040,
%U 1346269,3524578,0,-9227465,-9227465,14930352,39088169,0,-102334155,-102334155
%N Expansion of x/(x^4-3*x^3+4*x^2-2*x+1).
%H <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-4,3,-1).
%F a(5*n + 1) = F(5*n + 1), a(5*n + 2) = F(5*n + 3), a(5*n + 3) = 0, a(5*n - 1) = a(5*n) = -F(5*n), where F = A000045 the Fibonacci sequence.
%F G.f.: x / (x^4 - 3*x^3 + 4*x^2 - 2*x + 1). - _Michael Somos_, Apr 25 2003
%e x + 2*x^2 - 5*x^4 - 5*x^5 + 8*x^6 + 21*x^7 - 55*x^9 - 55*x^10 + 89*x^11 + ...
%t CoefficientList[Series[x/(x^4-3x^3+4x^2-2x+1),{x,0,40}],x] (* or *) LinearRecurrence[{2,-4,3,-1},{0,1,2,0},50] (* _Harvey P. Dale_, Aug 09 2020 *)
%o (PARI) {a(n) = local(x, y); x = fibonacci(n); y = fibonacci(n+1); [ -x, x, y, 0, -y][n%5 + 1]}
%Y Cf. A000045.
%K sign
%O 1,3
%A _Michael Somos_, Oct 07 1999
%E Zero prepended by _Harvey P. Dale_, Aug 09 2020
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