The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A048693 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A048693

Generalized Pellian with 2nd term equal to 6.
(history; published version)

#27 by Charles R Greathouse IV at Sat Jun 13 00:50:00 EDT 2015

LINKS

<a href="/index/Rec#order_02">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (2,1)

Discussion

Sat Jun 13

00:50

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

#26 by Charles R Greathouse IV at Sat Jun 13 00:27:43 EDT 2015

LINKS

<a href="/index/Rec#order_02">Index entries for to sequences related to with linear recurrences with constant coefficients</a>, signature (2,1)

Discussion

Sat Jun 13

00:27

OEIS Server: https://oeis.org/edit/global/2438

#25 by Jon E. Schoenfield at Fri Mar 20 08:30:16 EDT 2015

STATUS

editing

approved

#24 by Jon E. Schoenfield at Fri Mar 20 08:30:11 EDT 2015

AUTHOR

_Barry E. Williams_

STATUS

approved

editing

#23 by Bruno Berselli at Wed Jan 07 05:39:46 EST 2015

STATUS

reviewed

approved

#22 by Michel Marcus at Wed Jan 07 05:28:05 EST 2015

STATUS

proposed

reviewed

#21 by Jon E. Schoenfield at Wed Jan 07 05:12:38 EST 2015

STATUS

editing

proposed

#20 by Jon E. Schoenfield at Wed Jan 07 05:12:36 EST 2015

COMMENTS

Pisano period lengths: 1, 2, 8, 4, 12, 8, 6, 8, 24, 12, 24, 8, 28, 6, 24, 16, 16, 24, 40, 12, ... (is this A175181?) . - R. J. Mathar, Aug 10 2012

LINKS

<a href="/index/ReaRec#recLCCorder_02">Index entries for sequences related to linear recurrences with constant coefficients</a>, signature (2,1)

FORMULA

a(n) = 2*a(n-1) + a(n-2); a(0)=1, a(1)=6.

G.f.: (1+4*x)/(1 - 2*x - x^2). [From _- _Philippe Deléham_, Nov 03 2008]

a(n) = 4*A000129(n) + A000129(n+1). - R. J. Mathar, Aug 10 2012

MAPLE

with(combinat): a:=n->4*fibonacci(n-1, 2)+fibonacci(n, 2): seq(a(n), n=1..26); - _# _Zerinvary Lajos_, Apr 04 2008

MATHEMATICA

a[n_]:=(MatrixPower[{{1, 2}, {1, 1}}, n].{{5}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] [From _(* _Vladimir Joseph Stephan Orlovsky_, Feb 20 2010] *)

STATUS

approved

editing

#19 by N. J. A. Sloane at Wed Oct 09 02:23:05 EDT 2013

MAPLE

with(combinat): a:=n->4*fibonacci(n-1, 2)+fibonacci(n, 2): seq(a(n), n=1..26); - _Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), _, Apr 04 2008

Discussion

Wed Oct 09

02:23

OEIS Server: https://oeis.org/edit/global/1991

#18 by N. J. A. Sloane at Sun Sep 08 13:29:54 EDT 2013

FORMULA

G.f.: (1+4*x)/(1-2*x-x^2). [From _Philippe DELEHAM_, Deléham_, Nov 03 2008]

Discussion

Sun Sep 08

13:29

OEIS Server: https://oeis.org/edit/global/1938