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A052527 Expansion of (1-x)/(1-x-x^2-x^3+x^4). 2
1, 0, 1, 2, 2, 5, 8, 13, 24, 40, 69, 120, 205, 354, 610, 1049, 1808, 3113, 5360, 9232, 15897, 27376, 47145, 81186, 139810, 240765, 414616, 714005, 1229576, 2117432, 3646397, 6279400, 10813653, 18622018, 32068674, 55224945, 95101984 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

First differences of A116732 (shifted left 3 places). - R. J. Mathar, Nov 27 2011

LINKS

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 453

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

FORMULA

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

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

a(n) = Sum_{alpha = RootOf(1-x-x^2-x^3+x^4)} (1/39)*(2 + 11*alpha - 4*alpha^2 - alpha^3)*alpha^(-1-n).

MAPLE

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

MATHEMATICA

LinearRecurrence[{1, 1, 1, -1}, {1, 0, 1, 2}, 40] (* G. C. Greubel, May 13 2019 *)

PROG

(PARI) my(x='x+O('x^40)); Vec((1-x)/(1-x-x^2-x^3+x^4)) \\ G. C. Greubel, May 13 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)/(1-x-x^2-x^3+x^4) )); // G. C. Greubel, May 13 2019

(Sage) ((1-x)/(1-x-x^2-x^3+x^4)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, May 13 2019

(GAP) a:=[1, 0, 1, 2];; for n in [5..40] do a[n]:=a[n-1]+a[n-2]+a[n-3] -a[n-4]; od; a; # G. C. Greubel, May 13 2019

CROSSREFS

Sequence in context: A126291 A056224 A293674 * A042982 A006367 A246807

Adjacent sequences:  A052524 A052525 A052526 * A052528 A052529 A052530

KEYWORD

easy,nonn

AUTHOR

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

EXTENSIONS

More terms from James A. Sellers, Jun 05 2000

STATUS

approved

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Last modified February 27 11:51 EST 2020. Contains 332305 sequences. (Running on oeis4.)