The On-Line Encyclopedia of Integer Sequences (OEIS)

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A108413

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

#9 by Michael De Vlieger at Mon Sep 23 16:15:24 EDT 2024

STATUS

reviewed

approved

#8 by Stefano Spezia at Mon Sep 23 15:22:32 EDT 2024

STATUS

proposed

reviewed

#7 by Michael Somos at Mon Sep 23 15:12:20 EDT 2024

STATUS

editing

proposed

#6 by Michael Somos at Mon Sep 23 15:11:24 EDT 2024

FORMULA

a(n) = -4*a(n-2) + - a(n-4) for n>3. - Colin Barker, Sep 07 2017

MATHEMATICA

a[ n_] := If[n<0, a[2-n], SeriesCoefficient[(1 + x + 5*x^2 + 2*x^3) / (1 + 4*x^2 + x^4), {x, 0, n}]]; (* Michael Somos, Sep 23 2024 *)

PROG

(PARI) {a(n) = if(n<0, n=2-n); polcoeff( (1 + x + 5*x^2 + 2*x^3) / (1 + 4*x^2 + x^4) + x*O(x^n), n)}; /* Michael Somos, Sep 23 2024 */

STATUS

approved

editing

Discussion

Mon Sep 23

15:12

Michael Somos: Added more info. I fixed the obvious sign error in Barker recursion.

#5 by Alois P. Heinz at Thu Sep 07 08:30:14 EDT 2017

STATUS

proposed

approved

#4 by Colin Barker at Thu Sep 07 08:11:25 EDT 2017

STATUS

editing

proposed

#3 by Colin Barker at Thu Sep 07 08:10:33 EDT 2017

NAME

Expansion of (1+x+5x^2+2x^3) / (1-4x^2+x^4).

DATA

1, 1, 1, -2, -5, 7, 19, -26, -71, 97, 265, -362, -989, 1351, 3691, -5042, -13775, 18817, 51409, -70226, -191861, 262087, 716035, -978122, -2672279, 3650401, 9973081, -13623482, -37220045, 50843527, 138907099, -189750626, -518408351, 708158977, 1934726305

LINKS

Colin Barker, <a href="/A108413/b108413.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 (0,-4,0,-1).

FORMULA

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

a(n) = 4*a(n-2) + a(n-4) for n>3. - Colin Barker, Sep 07 2017

PROG

(PARI) Vec((1 + x + 5*x^2 + 2*x^3) / (1 + 4*x^2 + x^4) + O(x^40)) \\ Colin Barker, Sep 07 2017

KEYWORD

sign,easy

STATUS

approved

editing

#2 by Charles R Greathouse IV at Wed Apr 30 01:29:21 EDT 2014

AUTHOR

_Ralf Stephan, _, Jun 05 2005

Discussion

Wed Apr 30

01:29

OEIS Server: https://oeis.org/edit/global/2169

#1 by N. J. A. Sloane at Tue Jul 19 03:00:00 EDT 2005

NAME

Expansion of (1+x+5x^2+2x^3)/(1-4x^2+x^4).

DATA

OFFSET

0,4

FORMULA

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

CROSSREFS

Unsigned values are in A002531.

KEYWORD

sign

AUTHOR

Ralf Stephan, Jun 05 2005

STATUS

approved