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A052969 Expansion of (1-x)/(1-x-2x^2+x^4). 1
1, 0, 2, 2, 5, 9, 17, 33, 62, 119, 226, 431, 821, 1564, 2980, 5677, 10816, 20606, 39258, 74793, 142493, 271473, 517201, 985354, 1877263, 3576498, 6813823, 12981465, 24731848, 47118280, 89768153, 171023248, 325827706, 620755922, 1182643181 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..34.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1041

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

FORMULA

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

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

Sum(1/283*(29*_alpha+28*_alpha^3-76*_alpha^2+55)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z^2+_Z^4-_Z))

a(n)+a(n-1) = A052535(n). - R. J. Mathar, Nov 28 2011

MAPLE

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

MATHEMATICA

CoefficientList[Series[(1-x)/(1-x-2x^2+x^4), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 2, 0, -1}, {1, 0, 2, 2}, 40] (* Harvey P. Dale, Oct 20 2017 *)

CROSSREFS

Sequence in context: A212812 A214727 A302483 * A002990 A060405 A003228

Adjacent sequences:  A052966 A052967 A052968 * A052970 A052971 A052972

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 August 26 03:21 EDT 2019. Contains 326324 sequences. (Running on oeis4.)