A052532 Expansion of (1-x)/(1-x-x^3-x^4+x^5).

1, 0, 0, 1, 2, 1, 2, 5, 7, 8, 14, 24, 34, 49, 79, 123, 182, 276, 429, 655, 990, 1513, 2321, 3537, 5385, 8229, 12574, 19175, 29252, 44670, 68190, 104043, 158790, 242398, 369961, 564604, 861749, 1315318, 2007485, 3063877, 4676340, 7137394, 10893438

Offset

0,5

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 462

Index entries for linear recurrences with constant coefficients, signature (1,0,1,1,-1).

Formula

G.f.: (1 - x)/(1 - x - x^3 - x^4 + x^5).

a(n) = a(n-1) + a(n-3) + a(n-4) - a(n-5), with a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=2.

a(n) = Sum_{alpha = RootOf(1-x-x^3-x^4+x^5)} (1/8519)*(138 + 2003*alpha - 346*alpha^2 - 444*alpha^3 + 11*alpha^4)*alpha^(-1-n).

Maple

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

Mathematica

CoefficientList[Series[(1-x)/(1-x-x^3-x^4+x^5), {x, 0, 50}], x] (* Vincenzo Librandi, Apr 28 2014 *)
LinearRecurrence[{1, 0, 1, 1, -1}, {1, 0, 0, 1, 2}, 50] (* Harvey P. Dale, May 12 2018 *)

Prog

(PARI) my(x='x+O('x^50)); Vec((1-x)/(1-x-x^3-x^4+x^5)) \\ G. C. Greubel, May 09 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1-x)/(1-x-x^3-x^4+x^5) )); // G. C. Greubel, May 09 2019
(Sage) ((1-x)/(1-x-x^3-x^4+x^5)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, May 09 2019
(GAP) a:=[1, 0, 0, 1, 2];; for n in [6..50] do a[n]:=a[n-1]+a[n-3]+a[n-4] -a[n-5]; od; a; # G. C. Greubel, May 09 2019

Crossrefs

Sequence in context: A120898 A153910 A208021 * A006702 A129394 A214899

Adjacent sequences: A052529 A052530 A052531 * A052533 A052534 A052535

Keyword

easy,nonn

Author

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

Extensions

More terms from James A. Sellers, Jun 05 2000

Status

approved