OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-1,2).
FORMULA
O.g.f.: (1-x)^2*(1-3*x)/((2*x-1)*(1+x)*(x^2-x+1)). - R. J. Mathar, Jul 22 2008
a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4). - G. C. Greubel, Oct 07 2016
MAPLE
seq(coeff(series((1-x)^2*(1-3*x)/((2*x-1)*(1+x)*(x^2-x+1)), x, n+1), x, n), n = 0 .. 40); # G. C. Greubel, Nov 21 2019
MATHEMATICA
LinearRecurrence[{2, 0, -1, 2}, {-1, 3, -1, 2}, 40] (* G. C. Greubel, Oct 07 2016 *)
PROG
(PARI) my(x='x+O('x^40)); Vec((1-x)^2*(1-3*x)/((2*x-1)*(1+x)*(x^2-x+1))) \\ G. C. Greubel, Nov 21 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)^2*(1-3*x)/((2*x-1)*(1+x)*(x^2-x+1)) )); // G. C. Greubel, Nov 21 2019
(Sage)
def A135261_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1-x)^2*(1-3*x)/((2*x-1)*(1+x)*(x^2-x+1))).list()
A135261_list(40) # G. C. Greubel, Nov 21 2019
(GAP) a:=[-1, 2, -1, 2];; for n in [5..40] do a[n]:=2*a[n-1] -a[n-3] +2*a[n-4]; od; a; # G. C. Greubel, Nov 21 2019
CROSSREFS
KEYWORD
sign
AUTHOR
Paul Curtz, Dec 01 2007
EXTENSIONS
Edited and extended by R. J. Mathar, Jul 22 2008
STATUS
approved