The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A052546

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A052546

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

#26 by Charles R Greathouse IV at Thu Sep 08 08:44:59 EDT 2022

PROG

(MAGMAMagma) 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

Discussion

Thu Sep 08

08:44

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

#25 by Alois P. Heinz at Thu May 09 03:34:27 EDT 2019

STATUS

proposed

approved

#24 by Sean A. Irvine at Thu May 09 01:19:48 EDT 2019

STATUS

editing

proposed

#23 by Sean A. Irvine at Thu May 09 01:19:43 EDT 2019

FORMULA

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), alpha=RootOf(1-x-2*x^3+2*x^4-x^2)).

STATUS

proposed

editing

#22 by Sean A. Irvine at Thu May 09 01:14:23 EDT 2019

STATUS

editing

proposed

#21 by Sean A. Irvine at Thu May 09 01:14:19 EDT 2019

FORMULA

a(n) = Sum(-1/353 * (-18-106*_alpha+33*_alpha^2+28*_alpha^3) *_ alpha^(-1-n), _alpha=RootOf(1-_Zx-2*_Zx^3+2*_Zx^4-_Zx^2)).

STATUS

reviewed

editing

#20 by Michel Marcus at Thu May 09 00:43:53 EDT 2019

STATUS

proposed

reviewed

#19 by G. C. Greubel at Wed May 08 23:17:02 EDT 2019

STATUS

editing

proposed

#18 by G. C. Greubel at Wed May 08 23:16:20 EDT 2019

NAME

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

LINKS

G. C. Greubel, <a href="/A052546/b052546.txt">Table of n, a(n) for n = 0..1000</a>

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,2,-2).

FORMULA

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

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

a(n) = Sum(-1/353*(-18-106*_alpha+33*_alpha^2+28*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-_Z-2*_Z^3+2*_Z^4-_Z^2)).

MAPLE

spec := [S, {S=Sequence(Prod(Z, Z, Union(Z, Z, Sequence(Z))))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..2040);

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

STATUS

approved

editing

#17 by Harvey P. Dale at Sun Jul 02 13:34:33 EDT 2017

STATUS

editing

approved