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A052973 Expansion of ( 1-x ) / ( 1-x-3*x^2+x^3 ). 3
1, 0, 3, 2, 11, 14, 45, 76, 197, 380, 895, 1838, 4143, 8762, 19353, 41496, 90793, 195928, 426811, 923802, 2008307, 4352902, 9454021, 20504420, 44513581, 96572820, 209609143, 454814022, 987068631, 2141901554, 4648293425 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1045

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

FORMULA

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

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

Sum(-1/74*(1-34*_alpha+9*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-_Z-3*_Z^2+_Z^3))

MAPLE

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

CROSSREFS

Sequence in context: A134426 A122672 A194608 * A087956 A116391 A087629

Adjacent sequences:  A052970 A052971 A052972 * A052974 A052975 A052976

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 December 4 17:24 EST 2016. Contains 278755 sequences.