OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 890
Index entries for linear recurrences with constant coefficients, signature (2,0,1).
FORMULA
G.f.: (1-x^3)/(1-2*x-x^3).
a(n) = 2*a(n-1) + a(n-3), with a(0)=1, a(1)=2, a(2)=4, a(3)=8.
a(n) = Sum_{alpha=RootOf(-1 + 2*z + z^3)} (2/59)*(12 -8*alpha + 9*alpha^2)*alpha^(-1-n).
MAPLE
spec := [S, {S=Sequence(Prod(Sequence(Prod(Z, Z, Z)), Union(Z, Z)))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
Join[{1}, LinearRecurrence[{2, 0, 1}, {2, 4, 8}, 30]] (* Harvey P. Dale, Jun 07 2012 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1-x^3)/(1-2*x-x^3)) \\ G. C. Greubel, Oct 15 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-x^3)/(1-2*x-x^3) )); // G. C. Greubel, Oct 15 2019
(Sage)
def A052910_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1-x^3)/(1-2*x-x^3)).list()
A052910_list(30) # G. C. Greubel, Oct 15 2019
(GAP) a:=[2, 4, 8];; for n in [4..30] do a[n]:=2*a[n-1]+a[n-3]; od; Concatenation([1], a); # G. C. Greubel, Oct 15 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