A052932 Expansion of (1-x)/(1 - 2*x - x^4 + x^5).

1, 1, 2, 4, 9, 18, 37, 76, 157, 323, 665, 1369, 2819, 5804, 11950, 24604, 50658, 104301, 214748, 442150, 910354, 1874351, 3859149, 7945700, 16359604, 33683205, 69351208, 142788967, 293991838, 605307277, 1246282557, 2566002873

Offset

0,3

Comments

Equals INVERT transform of (1, 1, 1, 2, 1, 1, 1, 1, ...). - Gary W. Adamson, Apr 27 2009

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 918

Index entries for linear recurrences with constant coefficients, signature (2,0,0,1,-1).

Formula

G.f.: (1-x)/(1 - 2*x + x^5 - x^4).

a(n) = 2*a(n-1)*a(n-4) - a(n-5), with a(0)=a(1)=1, a(2)=2, a(3)=4, a(4)=9.

a(n) = Sum_{alpha=RootOf(1-2*z-z^4+z^5)} (1/11243)*(1807 + 1630*alpha -+ 319*alpha^2 + 428*alpha^3 - 1268*alpha^4)*alpha^(-1-n).

Maple

spec:= [S, {S=Sequence(Prod(Union(Sequence(Z), Prod(Z, Z, Z)), Z))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
seq(coeff(series((1-x)/(1-2*x+x^5-x^4), x, n+1), x, n), n = 0..40); # G. C. Greubel, Oct 17 2019

Mathematica

LinearRecurrence[{2, 0, 0, 1, -1}, {1, 1, 2, 4, 9}, 40] (* G. C. Greubel, Oct 17 2019 *)

Prog

(PARI) my(x='x+O('x^40)); Vec((1-x)/(1-2*x+x^5-x^4)) \\ G. C. Greubel, Oct 17 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)/(1-2*x+x^5-x^4) )); // G. C. Greubel, Oct 17 2019
(Sage)
def A052932_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1-x)/(1-2*x+x^5-x^4)).list()
A052932_list(40) # G. C. Greubel, Oct 17 2019
(GAP) a:=[1, 1, 2, 4, 9];; for n in [6..40] do a[n]:=2*a[n-1]+a[n-4]-a[n-5]; od; a; # G. C. Greubel, Oct 17 2019

Crossrefs

Sequence in context: A118255 A206927 A019299 * A018097 A327738 A215253

Adjacent sequences: A052929 A052930 A052931 * A052933 A052934 A052935

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Extensions

More terms from James A. Sellers, Jun 05 2000

Status

approved