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A052937 Expansion of (2-3*x-x^2)/((1-x)*(1-2*x-x^2)). 3
2, 3, 6, 13, 30, 71, 170, 409, 986, 2379, 5742, 13861, 33462, 80783, 195026, 470833, 1136690, 2744211, 6625110, 15994429, 38613966, 93222359, 225058682, 543339721, 1311738122, 3166815963, 7645370046, 18457556053, 44560482150, 107578520351, 259717522850 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 928

Index entries for linear recurrences with constant coefficients, signature (3,-1,-1).

FORMULA

G.f.: -(-2+3*x+x^2)/(-1+x)/(-1+2*x+x^2)

a(2)=6, a(1)=3, a(0)=2, -a(n)-2*a(n+1)+a(n+2)+2=0.

1+Sum(1/4*(1+_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z+_Z^2))

a(n) = A000129(n+1)+1, where A000129 are the Pell Numbers. - Graeme McRae, Aug 03 2006

a(n) = (1+(-(1-sqrt(2))^(1+n)+(1+sqrt(2))^(1+n))/(2*sqrt(2))). - Colin Barker, Mar 16 2016

MAPLE

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

MATHEMATICA

CoefficientList[Series[(2-3x-x^2)/((1-x)(1-2x-x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, -1, -1}, {2, 3, 6}, 40] (* Harvey P. Dale, May 27 2017 *)

PROG

(PARI) Vec((2-3*x-x^2)/((1-x)*(1-2*x-x^2)) + O(x^50)) \\ Colin Barker, Mar 16 2016

CROSSREFS

Cf. A001333.

Sequence in context: A079512 A280746 A174191 * A005554 A077212 A076836

Adjacent sequences:  A052934 A052935 A052936 * A052938 A052939 A052940

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 February 23 07:06 EST 2018. Contains 299473 sequences. (Running on oeis4.)