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A052982 Expansion of ( 1-x ) / ( 1-2*x-2*x^2+x^4 ). 0
1, 1, 4, 10, 27, 73, 196, 528, 1421, 3825, 10296, 27714, 74599, 200801, 540504, 1454896, 3916201, 10541393, 28374684, 76377258, 205587683, 553388489, 1489577660, 4009555040, 10792677717, 29051077025, 78197931824, 210488462658, 566580111247, 1525086070785 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..29.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1055

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

FORMULA

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

Recurrence: {a(1)=1, a(0)=1, a(2)=4, a(3)=10, a(n)-2*a(n+2)-2*a(n+3)+a(n+4)=0}.

Sum(-1/182*(-35*_alpha+2*_alpha^3+22*_alpha^2-25)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z-2*_Z^2+_Z^4)).

MAPLE

spec := [S, {S=Sequence(Prod(Union(Prod(Z, Z), Z), Union(Sequence(Z), Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);

MATHEMATICA

CoefficientList[Series[(1 - x)/(1 - 2*x - 2*x^2 + x^4), {x, 0, 30}], x] (* Wesley Ivan Hurt, Nov 13 2014 *)

LinearRecurrence[{2, 2, 0, -1}, {1, 1, 4, 10}, 30] (* Harvey P. Dale, Oct 03 2016 *)

CROSSREFS

Sequence in context: A192879 A077923 A183325 * A108672 A000495 A027067

Adjacent sequences:  A052979 A052980 A052981 * A052983 A052984 A052985

KEYWORD

easy,nonn

AUTHOR

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

EXTENSIONS

More terms from James A. Sellers, Jun 06 2000

STATUS

approved

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Last modified April 10 09:20 EDT 2021. Contains 342845 sequences. (Running on oeis4.)