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 (2,0,-1,2).
FORMULA
O.g.f.: x*(1-x)*(1 -3*x)/( (2*x-1)*(x+1)*(1 -x +x^2) ). - R. J. Mathar, Jul 22 2008
a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4). - G. C. Greubel, Oct 05 2016
MAPLE
seq(coeff(series(x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2)), x, n+1), x, n), n = 0 .. 35); # G. C. Greubel, Nov 21 2019
MATHEMATICA
LinearRecurrence[{2, 0, -1, 2}, {0, -1, 2, 1}, 35] (* G. C. Greubel, Oct 05 2016 *)
PROG
(PARI) concat(0, Vec(x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2)) + O(x^35))) \\ Michel Marcus, Oct 05 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 35); [0] cat Coefficients(R!( x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2)) )); // G. C. Greubel, Nov 21 2019
(Sage)
def A135259_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P(x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2))).list()
A135259_list(35) # G. C. Greubel, Nov 21 2019
(GAP) a:=[0, -1, 2, 1];; for n in [5..35] 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