A052990 Expansion of ( 1-x ) / ( 1-4*x-x^2+2*x^3 ).

1, 3, 13, 53, 219, 903, 3725, 15365, 63379, 261431, 1078373, 4448165, 18348171, 75684103, 312188253, 1287740773, 5311783139, 21910496823, 90378288885, 372800086085, 1537757639579, 6343074066631, 26164453733933, 107925373723205, 445179800493491

Offset

0,2

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1064

Index entries for linear recurrences with constant coefficients, signature (4,1,-2).

Formula

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

Recurrence: {a(0)=1, a(1)=3, a(2)=13, 2*a(n)-a(n+1)-4*a(n+2)+a(n+3)=0}

Sum(-1/142*(-22+18*r^2-21*r)*r^(-1-n) where r=RootOf(1-4*_Z-_Z^2+2*_Z^3))

Maple

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

Mathematica

LinearRecurrence[{4, 1, -2}, {1, 3, 13}, 40] (* Vincenzo Librandi, Jun 23 2012 *)
CoefficientList[Series[(1-x)/(1-4x-x^2+2x^3), {x, 0, 40}], x] (* Harvey P. Dale, Jan 15 2022 *)

Prog

(Magma) I:=[1, 3, 13]; [n le 3 select I[n] else 4*Self(n-1)+Self(n-2)-2*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 23 2012

Crossrefs

Sequence in context: A342815 A072197 A065838 * A151209 A151210 A151211

Adjacent sequences: A052987 A052988 A052989 * A052991 A052992 A052993

Keyword

easy,nonn

Author

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

Status

approved