A052546 Expansion of (1-x)/(1-x-x^2-2*x^3+2*x^4).

1, 0, 1, 3, 2, 7, 13, 18, 41, 71, 122, 239, 421, 762, 1417, 2543, 4642, 8495, 15389, 28082, 51177, 93047, 169610, 308847, 562197, 1024170, 1864841, 3395711, 6184498, 11261551, 20507789, 37346914, 68008809, 123848199, 225535258

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 482

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

Formula

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

a(n) = a(n-1) + a(n-2) + 2*a(n-3) - 2*a(n-4), with a(0)=1, a(1)=0, a(2)=1, a(3)=3.

a(n) = Sum_{alpha = RootOf(1-x-2*x^3+2*x^4-x^2)} (-1/353 * (-18-106*alpha+33*alpha^2+28*alpha^3) * alpha^(-1-n)).

Maple

spec := [S, {S=Sequence(Prod(Z, Z, Union(Z, Z, Sequence(Z))))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..40);

Mathematica

CoefficientList[Series[(1-x)/(1-x-x^2-2x^3+2x^4), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 1, 2, -2}, {1, 0, 1, 3}, 40] (* Harvey P. Dale, Jul 02 2017 *)

Prog

(PARI) my(x='x+O('x^40)); Vec((1-x)/(1-x-2*x^3+2*x^4-x^2)) \\ G. C. Greubel, May 08 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)/(1-x-2*x^3+2*x^4-x^2) )); // G. C. Greubel, May 08 2019
(Sage) ((1-x)/(1-x-2*x^3+2*x^4-x^2)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, May 08 2019
(GAP) a:=[1, 0, 1, 3];; for n in [5..40] do a[n]:=a[n-1]+a[n-2]+2*a[n-3] -2*a[n-4]; od; a; # G. C. Greubel, May 08 2019

Crossrefs

Sequence in context: A212189 A114647 A234750 * A260016 A320769 A358283

Adjacent sequences: A052543 A052544 A052545 * A052547 A052548 A052549

Keyword

easy,nonn

Author

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

Extensions

More terms from James A. Sellers, Jun 06 2000

Status

approved