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A077973
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Expansion of 1/(1+x-2*x^3).
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10
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1, -1, 1, 1, -3, 5, -3, -3, 13, -19, 13, 13, -51, 77, -51, -51, 205, -307, 205, 205, -819, 1229, -819, -819, 3277, -4915, 3277, 3277, -13107, 19661, -13107, -13107, 52429, -78643, 52429, 52429, -209715, 314573, -209715, -209715, 838861, -1258291, 838861, 838861, -3355443, 5033165, -3355443
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) = -a(n-1) +2*a(n-3). - Paul Curtz, Apr 23 2008
G.f.: G(0)/(2*(1-x^2)), where G(k)= 1 + 1/(1 - x*(k+1)/(x*(k+2) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 25 2013
a(n) = (-1)^n * Sum_{k=1..floor((n+2)/2)} binomial(n+2-2*k, k-1)*(-2)^(k-1). - Taras Goy, Sep 18 2019
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MATHEMATICA
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LinearRecurrence[{-1, 0, 2}, {1, -1, 1}, 50] (* or *) CoefficientList[Series[ 1/(1+x-2x^3), {x, 0, 50}], x] (* Harvey P. Dale, Jun 09 2017 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1+x-2*x^3) )); // G. C. Greubel, Jun 24 2019
(Sage) (1/(1+x-2*x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 24 2019
(GAP) a:=[1, -1, 1];; for n in [4..50] do a[n]:=-a[n-1]+2*a[n-3]; od; a; # G. C. Greubel, Jun 24 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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