A052985 Expansion of ( 1-x ) / ( 1-3*x+x^2-x^3+x^4 ).

1, 2, 5, 14, 38, 103, 280, 761, 2068, 5620, 15273, 41506, 112797, 306538, 833050, 2263903, 6152400, 16719809, 45437880, 123482328, 335576513, 911965282, 2478363781, 6735220246, 18303685726, 49742235431, 135179877032

Offset

0,2

Links

Table of n, a(n) for n=0..26.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1059

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

Formula

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

Recurrence: {a(0)=1, a(1)=2, a(2)=5, a(3)=14, a(n)-a(n+1)+a(n+2)-3*a(n+3)+a(n+4)=0}

Sum(-1/1099*(-270-11*_alpha+141*_alpha^3-104*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-3*_Z-_Z^3+_Z^4+_Z^2))

Maple

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

Crossrefs

Sequence in context: A172259 A292327 A084085 * A052945 A026288 A006574

Adjacent sequences: A052982 A052983 A052984 * A052986 A052987 A052988

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Extensions

More terms from James A. Sellers, Jun 05 2000

Status

approved