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A078029
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Expansion of (1-x)/(1-2*x^3).
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1
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1, -1, 0, 2, -2, 0, 4, -4, 0, 8, -8, 0, 16, -16, 0, 32, -32, 0, 64, -64, 0, 128, -128, 0, 256, -256, 0, 512, -512, 0, 1024, -1024, 0, 2048, -2048, 0, 4096, -4096, 0, 8192, -8192, 0, 16384, -16384, 0, 32768, -32768, 0, 65536, -65536, 0, 131072, -131072, 0, 262144, -262144, 0, 524288, -524288, 0
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: (1-x)/(1-2*x^3).
a(n) = (-1)^floor(4n/3)*(2-2*0^mod(n+1,3))^floor((n+1)/3). - Wesley Ivan Hurt, May 09 2015
a(n) = (4^(n/6)/6)*(2 - 2^(2/3) + 2^(5/3)*sin(Pi*(2*n/3 + 5/6)) - 4*sin(Pi*(2*n/3 + 3/2))). - Eric Simon Jacob, Jul 14 2024
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MAPLE
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MATHEMATICA
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CoefficientList[Series[(1-x)/(1-2*x^3), {x, 0, 60}], x] (* Vincenzo Librandi, May 10 2015 *)
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PROG
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(PARI) my(x='x+O('x^60)); Vec((1-x)/(1-2*x^3)) \\ G. C. Greubel, Aug 05 2019
(Sage) ((1-x)/(1-2*x^3)).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Aug 05 2019
(GAP) a:=[1, -1, 0];; for n in [4..60] do a[n]:=2*a[n-3]; od; a; # G. C. Greubel, Aug 05 2019
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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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STATUS
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approved
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