The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A041115 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A041115

Denominators of continued fraction convergents to sqrt(66).
(history; published version)

#32 by Charles R Greathouse IV at Thu Sep 08 08:44:54 EDT 2022

PROG

(MAGMAMagma) I:=[1, 8, 129, 1040]; [n le 4 select I[n] else 130*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 11 2013

Discussion

Thu Sep 08

08:44

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

#31 by Michel Marcus at Mon Feb 24 01:14:40 EST 2020

STATUS

reviewed

approved

#30 by Joerg Arndt at Mon Feb 24 01:09:51 EST 2020

STATUS

proposed

reviewed

#29 by M. F. Hasler at Sun Feb 23 16:56:49 EST 2020

STATUS

editing

proposed

#28 by M. F. Hasler at Sun Feb 23 16:56:37 EST 2020

FORMULA

a(2n) = A041495(2n), a(2n+1) = A041495(2n+1)*2. - M. F. Hasler, Feb 23 2020

CROSSREFS

Cf. A041114, A041495.

STATUS

approved

editing

#27 by Michel Marcus at Mon Sep 04 05:08:33 EDT 2017

STATUS

editing

approved

#26 by Michel Marcus at Mon Sep 04 05:08:29 EDT 2017

LINKS

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,130,0,-1).

STATUS

reviewed

editing

#25 by Joerg Arndt at Mon Sep 04 04:57:06 EDT 2017

STATUS

proposed

reviewed

#24 by Jon E. Schoenfield at Mon Sep 04 04:50:00 EDT 2017

STATUS

editing

proposed

#23 by Jon E. Schoenfield at Mon Sep 04 04:49:54 EDT 2017

FORMULA

a(n) = 16*a(n-1) + a(n-2) for n >= 2 even and a(n) = 8*a(n-1) + a(n-2) for n >= 2 odd. - _Nathaniel Johnston, _, Jun 26 2011

From Colin Barker, Feb 28 2013: (Start)

a(n) = 130*a(n-2) - a(n-4).

a(n) = 130*a(n-2) - a(n-4). G.f.: -(x^2 - 8*x - 1) / (x^4 - 130*x^2 + 1). - _Colin Barker_, Feb 28 2013(End)

MAPLE

a := proc(n) option remember: if(n<=1)then return (n+1)^3: fi: if(n mod 2 = 0)then return 16*a(n-1) + a(n-2): else return 8*a(n-1) + a(n-2): fi: end: seq(a(n), n=0..20); # _Nathaniel Johnston, _, Jun 26 2011

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing