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A051792 a(n) = (-1)^(n-1)*(a(n-1) - a(n-2)), a(1)=1, a(2)=1.

%I A051792 #23 Dec 07 2022 22:27:22
%S A051792 1,1,0,1,1,0,-1,1,2,-1,-3,2,5,-3,-8,5,13,-8,-21,13,34,-21,-55,34,89,
%T A051792 -55,-144,89,233,-144,-377,233,610,-377,-987,610,1597,-987,-2584,1597,
%U A051792 4181,-2584,-6765,4181,10946,-6765,-17711,10946,28657,-17711,-46368
%N A051792 a(n) = (-1)^(n-1)*(a(n-1) - a(n-2)), a(1)=1, a(2)=1.
%H A051792 G. C. Greubel, <a href="/A051792/b051792.txt">Table of n, a(n) for n = 1..1000</a>
%H A051792 <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%H A051792 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,-1,0,1).
%F A051792 a(3-n) = A053602(n).
%F A051792 From _Michael Somos_: (Start)
%F A051792 G.f.: x*(1 + x + x^2 + 2*x^3)/(1 + x^2 - x^4).
%F A051792 a(n) = -a(n-2) + a(n-4). (End)
%F A051792 a(n) = b(n-1) + b(n-2) + b(n-3) + 2*b(n-4), where b(n) = i^n * A079977(n). - _G. C. Greubel_, Dec 06 2022
%t A051792 LinearRecurrence[{0,-1,0,1},{1,1,0,1},60] (* _Harvey P. Dale_, May 08 2017 *)
%o A051792 (PARI) a(n)=fibonacci((3-n)\2+(3-n)%2*2)
%o A051792 (Sage)
%o A051792 def A051792():
%o A051792     x, y, b = 1, 1, true
%o A051792     while True:
%o A051792         yield x
%o A051792         x, y = y, x - y
%o A051792         y = -y if b else y
%o A051792         b = not b
%o A051792 a = A051792()
%o A051792 print([next(a) for _ in range(51)]) # _Peter Luschny_, Mar 19 2020
%o A051792 (Magma) [Fibonacci(1 -Floor((n-4)/2) -2*((n-4) mod 2)): n in [1..60]]; // _G. C. Greubel_, Dec 06 2022
%Y A051792 Cf. A000045, A053602.
%K A051792 easy,sign
%O A051792 1,9
%A A051792 Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 10 1999