The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A122069 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A122069

a(n) = 3*a(n-1) + 9*a(n-2) for n > 1, with a(0)=1, a(1)=3.
(history; published version)

#36 by Bruno Berselli at Sun Sep 15 06:50:58 EDT 2024

STATUS

reviewed

approved

#35 by Joerg Arndt at Sun Sep 15 04:43:01 EDT 2024

STATUS

proposed

reviewed

#34 by Jason Yuen at Sun Sep 15 04:14:07 EDT 2024

STATUS

editing

proposed

#33 by Jason Yuen at Sun Sep 15 04:12:57 EDT 2024

FORMULA

Limit_{n->oo} a(n+1)/a(n) -> = 3*((1+sqrt(5))/2 if n ->infinity.

STATUS

approved

editing

#32 by Joerg Arndt at Mon Jan 01 11:48:56 EST 2024

STATUS

editing

approved

#31 by Paolo P. Lava at Mon Jan 01 11:45:03 EST 2024

FORMULA

a(n) = (1/2)*((3/2)+(3/2)*sqrt(5))^n+(1/10)*((3/2)+(3/2)*sqrt(5))^n*sqrt(5)-(1/10)*sqrt(5)*((3/2)-(3/2)*sqrt(5))^n+(1/2)*((3/2)-(3/2)*sqrt(5))^n, with n >= 0. - Paolo P. Lava, Nov 19 2008

STATUS

approved

editing

#30 by Charles R Greathouse IV at Thu Sep 08 08:45:28 EDT 2022

PROG

(MAGMAMagma) [3^n*Fibonacci(n+1): n in [0..25]]; // G. C. Greubel, Oct 03 2019

Discussion

Thu Sep 08

08:45

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

#29 by Harvey P. Dale at Tue Apr 28 12:57:49 EDT 2020

STATUS

editing

approved

#28 by Harvey P. Dale at Tue Apr 28 12:57:47 EDT 2020

MATHEMATICA

LinearRecurrence[{3, 9}, {1, 3}, 30] (* Harvey P. Dale, Apr 28 2020 *)

STATUS

approved

editing

#27 by N. J. A. Sloane at Sat Dec 07 12:18:25 EST 2019

PROG

(Sage) [lucas_number1(n, 3, -9) for n in xrangerange(1, 23)] # Zerinvary Lajos, Apr 22 2009

Discussion

Sat Dec 07

12:18

OEIS Server: https://oeis.org/edit/global/2837