OFFSET
0,5
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 934
Index entries for linear recurrences with constant coefficients, signature (0,2,1,0,-1).
FORMULA
G.f.: (1-x^2)/(1-2*x^2-x^3+x^5).
a(n) = 2*a(n-2) + a(n-3) - a(n-5).
a(n) = Sum_{alpha=RootOf(1-2*z^2-z^3+z^5)} (1/4511)*(330 +1089*alpha -224*alpha^2 -167*alpha^3 -100*alpha^4)*alpha^(-1-n).
MAPLE
spec := [S, {S=Sequence(Prod(Z, Z, Union(Z, Sequence(Prod(Z, Z)))))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
seq(coeff(series((1-x^2)/(1-2*x^2-x^3+x^5), x, n+1), x, n), n = 0..50); # G. C. Greubel, Oct 18 2019
MATHEMATICA
CoefficientList[Series[(1-x^2)/(1-2x^2-x^3+x^5), {x, 0, 50}], x] (* or *) LinearRecurrence[{0, 2, 1, 0, -1}, {1, 0, 1, 1, 2}, 50] (* Harvey P. Dale, May 27 2012 *)
PROG
(PARI) my(x='x+O('x^50)); Vec((1-x^2)/(1-2*x^2-x^3+x^5)) \\ G. C. Greubel, Oct 18 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1-x^2)/(1-2*x^2-x^3+x^5) )); // G. C. Greubel, Oct 18 2019
(Sage)
def A052943_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1-x^2)/(1-2*x^2-x^3+x^5)).list()
A052943_list(50) # G. C. Greubel, Oct 18 2019
(GAP) a:=[1, 0, 1, 1, 2];; for n in [6..50] do a[n]:=2*a[n-2]+a[n-3]-a[n-5]; od; a; # G. C. Greubel, Oct 18 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from James A. Sellers, Jun 05 2000
STATUS
approved