OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-1,1,-2).
FORMULA
a(n) = (-1)^n * A077947(n).
G.f.: Q(0)/2 , where Q(k) = 1 + 1/(1 - x*(4*k+1 - x + 2*x^2 )/( x*(4*k+3 - x + 2*x^2 ) - 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 09 2013
MATHEMATICA
LinearRecurrence[{-1, 1, -2}, {1, -1, 2}, 40] (* or *) CoefficientList[ Series[1/(1+x-x^2+2*x^3), {x, 0, 40}], x] (* G. C. Greubel, Jun 24 2019 *)
PROG
(PARI) Vec(1/(1+x-x^2+2*x^3)+O(x^40)) \\ Charles R Greathouse IV, Sep 27 2012
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1+x-x^2+2*x^3) )); // G. C. Greubel, Jun 24 2019
(Sage) (1/(1+x-x^2+2*x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 24 2019
(GAP) a:=[1, -1, 2];; for n in [4..40] do a[n]:=-a[n-1]+a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Jun 24 2019
CROSSREFS
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved