A077940 Expansion of 1/(1-2*x+2*x^3).
1, 2, 4, 6, 8, 8, 4, -8, -32, -72, -128, -192, -240, -224, -64, 352, 1152, 2432, 4160, 6016, 7168, 6016, 0, -14336, -40704, -81408, -134144, -186880, -210944, -153600, 66560, 555008, 1417216, 2701312, 4292608, 5750784, 6098944, 3612672, -4276224, -20750336, -48726016, -88899584
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,0,-2).
Crossrefs
Cf. A077988.
Programs
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GAP
a:=[1,2,4];; for n in [4..50] do a[n]:=2*(a[n-1]-a[n-3]); od; a; # G. C. Greubel, Jun 26 2019
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Magma
R
:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-2*x+2*x^3) )); // G. C. Greubel, Jun 26 2019 -
Mathematica
LinearRecurrence[{2,0,-2}, {1,2,4}, 50] (* or *) CoefficientList[Series[ 1/(1-2*x+2*x^3), {x,0,50}], x] (* G. C. Greubel, Jun 26 2019 *) -
PARI
my(x='x+O('x^50)); Vec(1/(1-2*x+2*x^3)) \\ G. C. Greubel, Jun 26 2019 -
Sage
(1/(1-2*x+2*x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 26 2019
Formula
a(n) = (-1)^n * A077988(n). - R. J. Mathar, Feb 04 2014
Comments