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Revision History for A123879

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A123879

Expansion of (1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4).
(history; published version)

#12 by Charles R Greathouse IV at Thu Sep 08 08:45:28 EDT 2022

PROG

(MAGMAMagma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4) )); // G. C. Greubel, Aug 08 2019

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#11 by Joerg Arndt at Thu Aug 08 04:26:28 EDT 2019

STATUS

reviewed

approved

#10 by Michel Marcus at Thu Aug 08 03:53:37 EDT 2019

STATUS

proposed

reviewed

#9 by G. C. Greubel at Thu Aug 08 03:49:27 EDT 2019

STATUS

editing

proposed

#8 by G. C. Greubel at Thu Aug 08 03:49:17 EDT 2019

PROG

(PARI) my(x='x+O('x^3040)); Vec((1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4)) \\ G. C. Greubel, Aug 08 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 3040); Coefficients(R!( (1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4) )); // G. C. Greubel, Aug 08 2019

STATUS

proposed

editing

Discussion

Thu Aug 08

03:49

G. C. Greubel: Done.

#7 by G. C. Greubel at Thu Aug 08 03:30:03 EDT 2019

STATUS

editing

proposed

Discussion

Thu Aug 08

03:44

Michel Marcus: 40 terms (rather than 30) in pari & magma ?

#6 by G. C. Greubel at Thu Aug 08 03:30:00 EDT 2019

LINKS

G. C. Greubel, <a href="/A123879/b123879.txt">Table of n, a(n) for n = 0..1000</a>

#5 by G. C. Greubel at Thu Aug 08 03:27:53 EDT 2019

CROSSREFS

Cf. A123878, A123880.

#4 by G. C. Greubel at Thu Aug 08 03:27:02 EDT 2019

PROG

def A077952_A123879_list(prec):

A077952_A123879_list(40) # G. C. Greubel, Aug 08 2019

#3 by G. C. Greubel at Thu Aug 08 03:26:03 EDT 2019

NAME

Expansion of (1-2x2*x+2x2*x^2-x^3)/(1-3x3*x+5x5*x^2-3x3*x^3+x^4).

LINKS

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-5,3,-1).

FORMULA

a(n) =sum Sum_{k=0..n, sum} Sum_{j=0..n, } (-1)^(j-k)*C(n+j,2j2*j)*C(j+k,2k)2*(-1)^(j-k)}}.

MAPLE

seq(coeff(series((1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4), x, n+1), x, n), n = 0 .. 40); # G. C. Greubel, Aug 08 2019

MATHEMATICA

LinearRecurrence[{3, -5, 3, -1}, {1, 1, 0, -3}, 40] (* G. C. Greubel, Aug 08 2019 *)

PROG

(PARI) my(x='x+O('x^30)); Vec((1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4)) \\ G. C. Greubel, Aug 08 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4) )); // G. C. Greubel, Aug 08 2019

(Sage)

def A077952_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P((1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4)).list()

A077952_list(40) # G. C. Greubel, Aug 08 2019

(GAP) a:=[1, 1, 0, -3];; for n in [5..40] do a[n]:=3*a[n-1]-5*a[n-2]+3*a[n-3]-a[n-4]; od; a; # G. C. Greubel, Aug 08 2019

CROSSREFS

Cf. A123880.

STATUS

approved

editing