OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 916
Index entries for linear recurrences with constant coefficients, signature (1,2,2,-2).
FORMULA
G.f.: (1-x)/(1 - x - 2*x^2 - 2*x^3 + 2*x^4).
a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3) - 2*a(n-4).
a(n) = Sum_{alpha=RootOf(1 - z - 2*z^2 - 2*z^3 + 2*z^4)} (1/1651)*(101 + 469*alpha - 236*alpha^2 - 30*alpha^3)*alpha^(-1-n).
MAPLE
spec:= [S, {S=Sequence(Prod(Union(Sequence(Z), Z), Union(Z, Z), Z))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
seq(coeff(series((1-x)/(1-x-2*x^3+2*x^4-2*x^2), x, n+1), x, n), n = 0 .. 40); # G. C. Greubel, Oct 17 2019
MATHEMATICA
LinearRecurrence[{1, 2, 2, -2}, {1, 0, 2, 4}, 40] (* G. C. Greubel, Oct 17 2019 *)
PROG
(PARI) my(x='x+O('x^40)); Vec((1-x)/(1-x-2*x^3+2*x^4-2*x^2)) \\ G. C. Greubel, Oct 17 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)/(1-x-2*x^3+2*x^4-2*x^2) )); // G. C. Greubel, Oct 17 2019
(Sage)
def A052930_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1-x)/(1-x-2*x^3+2*x^4-2*x^2)).list()
A052930_list(40) # G. C. Greubel, Oct 17 2019
(GAP) a:=[1, 0, 2, 4];; for n in [5..40] do a[n]:=a[n-1]+2*a[n-2]+2*a[n-3] -2*a[n-4]; od; a; # G. C. Greubel, Oct 17 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