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A052949 Expansion of (2-4x+x^3)/((1-x)(1-2x-x^2+x^3)). 1
2, 2, 4, 7, 15, 32, 71, 158, 354, 794, 1783, 4005, 8998, 20217, 45426, 102070, 229348, 515339, 1157955, 2601900, 5846415, 13136774, 29518062, 66326482, 149034251, 334876921, 752461610, 1690765889, 3799116466, 8536537210, 19181424996 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..30.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1008

Index entries for linear recurrences with constant coefficients, signature (3,-1,-2,1).

FORMULA

G.f.: -(2-4*x+x^3)/(x^3-x^2-2*x+1)/(-1+x)

Recurrence: {a(2)=4, a(1)=2, a(3)=7, a(0)=2, -a(n)+a(n+1)+2*a(n+2)-a(n+3)-1=0}

1+Sum(-1/7*(-2*_alpha+_alpha^2-1)*_alpha^(-1-n), _alpha=RootOf(_Z^3-_Z^2-2*_Z+1))

MAPLE

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

CROSSREFS

Equals A006356(n-1) + 1, n>0.

Sequence in context: A049906 A014265 A153967 * A014266 A032441 A238184

Adjacent sequences:  A052946 A052947 A052948 * A052950 A052951 A052952

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 April 20 09:03 EDT 2019. Contains 322307 sequences. (Running on oeis4.)