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A052946 Expansion of (1-x)^2/(1-3*x+2*x^3-x^4). 2
1, 1, 4, 10, 29, 80, 224, 624, 1741, 4855, 13541, 37765, 105326, 293751, 819264, 2284905, 6372539, 17772840, 49567974, 138243749, 385558106, 1075311210, 2999014106, 8364169855, 23327445251, 65059618751, 181449530649 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1005

Index entries for linear recurrences with constant coefficients, signature (3,0,-2,1).

FORMULA

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

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

a(n) = Sum_{alpha=RootOf(-1+3*z-2*z^3+z^4)} (1/643)*(79 + 128*alpha - 133*alpha^2 + 40*alpha^3)*alpha^(-1-n).

MAPLE

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

seq(coeff(series((1-x)^2/(1-3*x+2*x^3-x^4), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 21 2019

MATHEMATICA

LinearRecurrence[{3, 0, -2, 1}, {1, 1, 4, 10}, 30] (* G. C. Greubel, Oct 21 2019 *)

PROG

(PARI) my(x='x+O('x^30)); Vec((1-x)^2/(1-3*x+2*x^3-x^4)) \\ G. C. Greubel, Oct 21 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-x)^2/(1-3*x+2*x^3-x^4) )); // G. C. Greubel, Oct 21 2019

(Sage)

def A052946_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P((1-x)^2/(1-3*x+2*x^3-x^4)).list()

A052946_list(30) # G. C. Greubel, Oct 21 2019

(GAP) a:=[1, 1, 4, 10];; for n in [5..30] do a[n]:=3*a[n-1]-2*a[n-3]+a[n-4]; od; a; # G. C. Greubel, Oct 21 2019

CROSSREFS

Sequence in context: A327590 A321344 A329156 * A026152 A025179 A116388

Adjacent sequences:  A052943 A052944 A052945 * A052947 A052948 A052949

KEYWORD

easy,nonn

AUTHOR

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

EXTENSIONS

More terms from James A. Sellers, Jun 06 2000

STATUS

approved

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Last modified July 13 15:18 EDT 2020. Contains 335688 sequences. (Running on oeis4.)