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Revision History for A093379

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A093379

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

#8 by Harvey P. Dale at Fri May 10 15:11:19 EDT 2019

STATUS

editing

approved

#7 by Harvey P. Dale at Fri May 10 15:11:15 EDT 2019

MATHEMATICA

CoefficientList[Series[x (1-2x-2x^2)/((1+x)(1-2x)(1-3x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{4, -1, -6}, {0, 1, 2, 5}, 40] (* Harvey P. Dale, May 10 2019 *)

STATUS

approved

editing

#6 by Charles R Greathouse IV at Sat Jun 13 00:51:19 EDT 2015

LINKS

<a href="/index/Rec#order_03">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (4,-1,-6).

Discussion

Sat Jun 13

00:51

OEIS Server: https://oeis.org/edit/global/2439

#5 by R. J. Mathar at Wed Dec 17 12:51:42 EST 2014

STATUS

editing

approved

#4 by R. J. Mathar at Wed Dec 17 12:34:00 EST 2014

LINKS

<a href="/index/Rec#order_03">Index to sequences with linear recurrences with constant coefficients</a>, signature (4,-1,-6).

FORMULA

a(n)=3^n/12-(-1)^n/12+2^n/3-0^n/3; a(n)=4a(n-1)-a(n-2)-6a(n-3). a(n)=A015518(n)/3+A000079(n)/3-0^n/3.

a(n)=4a(n-1)-a(n-2)-6a(n-3).

a(n)=A015518(n)/3+A000079(n)/3-0^n/3.

STATUS

approved

editing

#3 by Russ Cox at Fri Mar 30 18:58:55 EDT 2012

AUTHOR

_Paul Barry (pbarry(AT)wit.ie), _, Apr 28 2004

Discussion

Fri Mar 30

18:58

OEIS Server: https://oeis.org/edit/global/287

#2 by N. J. A. Sloane at Wed Sep 22 03:00:00 EDT 2004

CROSSREFS

Cf. A087432.

KEYWORD

easy,nonn,new

#1 by N. J. A. Sloane at Sat Jun 12 03:00:00 EDT 2004

NAME

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

DATA

0, 1, 2, 5, 12, 31, 82, 225, 632, 1811, 5262, 15445, 45652, 135591, 404042, 1206665, 3609072, 10805371, 32372422, 97029885, 290914892, 872395151, 2616486402, 7848061105, 23541387112, 70618568931, 211844521982, 635511196325

OFFSET

0,3

COMMENTS

Binomial transform is A085280, with leading zero.

FORMULA

a(n)=3^n/12-(-1)^n/12+2^n/3-0^n/3; a(n)=4a(n-1)-a(n-2)-6a(n-3). a(n)=A015518(n)/3+A000079(n)/3-0^n/3.

KEYWORD

easy,nonn

AUTHOR

Paul Barry (pbarry(AT)wit.ie), Apr 28 2004

STATUS

approved