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A052989

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

1, 0, 1, 1, 3, 3, 7, 10, 19, 29, 52, 84, 145, 239, 407, 678, 1146, 1918, 3232, 5421, 9121, 15314, 25749, 43252, 72701, 122146, 205282, 344931, 579662, 974038, 1636836, 2750523, 4622090, 7766989, 13051877, 21932553, 36855997, 61933449, 104074334

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OFFSET

0,5

LINKS

Table of n, a(n) for n=0..38.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1063

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

FORMULA

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

Recurrence: {a(1)=0, a(0)=1, a(2)=1, a(3)=1, a(4)=3, a(n)-a(n+1)-a(n+3)-a(n+4)+a(n+5) =0}

Sum(-1/8519*(-389-2111*_alpha+619*_alpha^2-358*_alpha^3+541*_alpha^4)*_alpha^(-1-n), _alpha=RootOf(1-_Z-_Z^2-_Z^4+_Z^5))

MAPLE

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

MATHEMATICA

CoefficientList[Series[(1-x)/(1-x-x^2-x^4+x^5), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 1, 0, 1, -1}, {1, 0, 1, 1, 3}, 40] (* Harvey P. Dale, Sep 01 2017 *)

CROSSREFS

Sequence in context: A013915 A136445 A326269 * A358823 A252750 A287274

Adjacent sequences: A052986 A052987 A052988 * A052990 A052991 A052992

KEYWORD

easy,nonn

AUTHOR

INRIA Encyclopedia of Combinatorial Structures, Jan 25 2000

EXTENSIONS

More terms from James Sellers, Jun 06 2000

STATUS

approved

URL: https://oeis.org/A052989

⇱ A052989 - OEIS