OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,-2).
FORMULA
G.f.: (1-x)/(1-x+2*x^3).
G.f.: G(0)/(2*(1+x)), where G(k)= 1 + 1/(1 - x*(k+1)/(x*(k+2) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 25 2013
MATHEMATICA
LinearRecurrence[{1, 0, -2}, {1, 0, 0}, 50] (* or *) CoefficientList[Series[ (1-x)/(1-x+2*x^3), {x, 0, 50}], x] (* G. C. Greubel, Jun 29 2019 *)
PROG
(PARI) my(x='x+O('x^50)); Vec((1-x)/(1-x+2*x^3)) \\ G. C. Greubel, Jun 29 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1-x)/(1-x+2*x^3) )); // G. C. Greubel, Jun 29 2019
(Sage) ((1-x)/(1-x+2*x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 29 2019
(GAP) a:=[1, 0, 0];; for n in [4..50] do a[n]:=a[n-1]-2*a[n-3]; od; a; # G. C. Greubel, Jun 29 2019
CROSSREFS
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved