The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A134068 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A134068

a(n) = 2*a(n-2) + 4*a(n-3), with initial terms 0, 3, 3.
(history; published version)

#12 by Charles R Greathouse IV at Thu Sep 08 08:45:32 EDT 2022

PROG

(MAGMAMagma) a:=[0, 3, 3]; [n le 3 select a[n] else 2*Self(n-2) + 4*Self(n-3):n in [1..35]]; // Marius A. Burtea, Jan 03 2020

(MAGMAMagma) R<x>:=PowerSeriesRing(Integers(), 35); [0] cat Coefficients(R!( 3*x*(1 + x)/((1 - 2*x)*(1 + 2*x + 2*x^2)))); // Marius A. Burtea, Jan 03 2020

Discussion

Thu Sep 08

08:45

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

#11 by Peter Luschny at Fri Jan 03 16:25:48 EST 2020

STATUS

proposed

approved

#10 by Marius A. Burtea at Fri Jan 03 16:08:44 EST 2020

STATUS

editing

proposed

#9 by Marius A. Burtea at Fri Jan 03 16:08:33 EST 2020

PROG

(MAGMA) a:=[0, 3, 3]: ; [n le 3 select a[n] else 2*Self(n-2) + 4*Self(n-3):n in [1..35]]; // Marius A. Burtea, Jan 03 2020

STATUS

proposed

editing

#8 by Marius A. Burtea at Fri Jan 03 16:06:28 EST 2020

STATUS

editing

proposed

#7 by Marius A. Burtea at Fri Jan 03 16:06:17 EST 2020

PROG

(MAGMA) a:=[0, 3, 3]: [n le 2 3 select a[n] else 2*Self(n-2) + 4*Self(n-3):n in [1..35]]; // Marius A. Burtea, Jan 03 2020

STATUS

proposed

editing

#6 by Marius A. Burtea at Fri Jan 03 16:02:20 EST 2020

STATUS

editing

proposed

#5 by Marius A. Burtea at Fri Jan 03 16:01:13 EST 2020

PROG

(MAGMA) a:=[0, 3, 3]: [n le 2 select a[n] else 2*Self(n-2) + 4*Self(n-3):n in [1..35]]; // Marius A. Burtea, Jan 03 2020

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 35); [0] cat Coefficients(R!( 3*x*(1 + x)/((1 - 2*x)*(1 + 2*x + 2*x^2)))); // Marius A. Burtea, Jan 03 2020

STATUS

proposed

editing

#4 by Andrew Howroyd at Fri Jan 03 15:47:25 EST 2020

STATUS

editing

proposed

#3 by Andrew Howroyd at Fri Jan 03 15:44:14 EST 2020

NAME

a(n) =2a 2*a(n-2) +4a 4*a(n-3), n > with initial terms 0, 3, 3.

DATA

0, 3, 3, 6, 18, 24, 60, 120, 216, 480, 912, 1824, 12483744, 7296, 14784, 29568, 58752, 118272, 235776, 471552, 944640, 1886208, 3775488, 7550976, 15095808, 30203904, 60395520, 120791040, 241606656, 483164160, 966377472, 1932754944, 3865411584, 7731019776, 15461842944

LINKS

Andrew Howroyd, <a href="/A134068/b134068.txt">Table of n, a(n) for n = 0..1000</a>

<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,4).

FORMULA

From Andrew Howroyd, Jan 03 2020: (Start)

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

a(n) = 3*A134136(n). (End)

PROG

(PARI) concat([0], Vec(3*(1 + x)/((1 - 2*x)*(1 + 2*x + 2*x^2)) + O(x^40))) \\ Andrew Howroyd, Jan 03 2020

CROSSREFS

Cf. A134136, A134654.

EXTENSIONS

a(12) corrected and terms a(13) and beyond from Andrew Howroyd, Jan 03 2020

STATUS

approved

editing