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A052930 Expansion of (1-x)/(1 - x - 2*x^2 - 2*x^3 + 2*x^4). 1
1, 0, 2, 4, 6, 18, 34, 74, 166, 346, 758, 1634, 3510, 7602, 16374, 35330, 76262, 164466, 354902, 765698, 1651910, 3564178, 7689590, 16590370, 35794086, 77225650, 166615382, 359474114, 775568006, 1673295698, 3610149174 (list; graph; refs; listen; history; text; internal format)
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

Sequence in context: A242765 A073664 A088174 * A098853 A023149 A085146

Adjacent sequences:  A052927 A052928 A052929 * A052931 A052932 A052933

KEYWORD

easy,nonn

AUTHOR

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

EXTENSIONS

More terms from James A. Sellers, Jun 05 2000

STATUS

approved

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Last modified October 25 19:28 EDT 2020. Contains 338012 sequences. (Running on oeis4.)