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A141576
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An alternating sequence of a difference type: a(0)=-1, a(1)=0, a(2)=1, a(n) = a(n-1) - 2*a(n-2) + a(n-3).
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1
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-1, 0, 1, 0, -2, -1, 3, 3, -4, -7, 4, 14, -1, -25, -9, 40, 33, -56, -82, 63, 171, -37, -316, -71, 524, 350, -769, -945, 943, 2064, -767, -3952, -354, 6783, 3539, -10381, -10676, 13625, 24596, -13330, -48897, 2359, 86823, 33208, -138079, -117672, 191694
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OFFSET
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0,5
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REFERENCES
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Martin Gardner, Mathematical Circus, Random House, New York, 1981, p. 165.
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LINKS
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FORMULA
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O.g.f.: (1-x+x^2)/(-1+x-2x^2+x^3).
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EXAMPLE
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-1 + x^2 - 2*x^4 - x^5 + 3*x^6 + 3*x^7 - 4*x^8 - 7*x^9 + ...
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MATHEMATICA
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Nest[Append[#, #[[-1]] - 2 #[[-2]] + #[[-3]]] &, {-1, 0, 1}, 44] (* Michael De Vlieger, Dec 17 2017 *)
LinearRecurrence[{1, -2, 1}, {-1, 0, 1}, 50] (* Harvey P. Dale, Feb 06 2024 *)
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PROG
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(MATLAB)
function y=fib(n)
%Generates difference sequence
fz(1)=-1; fz(2)=0; fz(3)=1;
for k=4:n
fz(k)=fz(k-1)-2*fz(k-2)+fz(k-3);
end
y=fz(n);
(PARI) x='x+O('x^99); Vec((1-x+x^2)/(-1+x-2*x^2+x^3)) \\ Altug Alkan, Dec 17 2017
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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Matt Wynne (mattwyn(AT)verizon.net), Aug 18 2008
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EXTENSIONS
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STATUS
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approved
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