A052981 Expansion of ( 1-x ) / ( 1-4*x-3*x^2+3*x^3 ).

1, 3, 15, 66, 300, 1353, 6114, 27615, 124743, 563475, 2545284, 11497332, 51934755, 234595164, 1059692925, 4786752927, 21622304991, 97670399970, 441188256072, 1992897309225, 9002142805206, 40663698380283, 183682530009075, 829714786761531, 3747915641932500

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1054

Index entries for linear recurrences with constant coefficients, signature (4,3,-3)

Formula

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

Recurrence: {a(0)=1, a(1)=3, a(2)=15, 3*a(n)-3*a(n+1)-4*a(n+2)+a(n+3)=0}.

Sum(-1/95*(-11-22*r+15*r^2)*r^(-1-n) where r=RootOf(1-4*_Z-3*_Z^2+3*_Z^3)).

Maple

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

Mathematica

LinearRecurrence[{4, 3, -3}, {1, 3, 15}, 40] (* Vincenzo Librandi, Jun 23 2012 *)

Prog

(Magma) I:=[1, 3, 15]; [n le 3 select I[n] else 4*Self(n-1)+3*Self(n-2) -3*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 23 2012

Crossrefs

Sequence in context: A144067 A001447 A106732 * A086200 A325586 A304276

Adjacent sequences: A052978 A052979 A052980 * A052982 A052983 A052984

Keyword

easy,nonn

Author

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

Status

approved