The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A162557 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A162557

a(n) = ((3+sqrt(3))*(4+sqrt(3))^n+(3-sqrt(3))*(4-sqrt(3))^n)/6.
(history; published version)

#30 by Charles R Greathouse IV at Thu Sep 08 08:45:46 EDT 2022

PROG

(MAGMAMagma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((3+r)*(4+r)^n+(3-r)*(4-r)^n)/6: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 13 2009

(MAGMAMagma) I:=[1, 5]; [n le 2 select I[n] else 8*Self(n-1)-13*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Aug 30 2016

Discussion

Thu Sep 08

08:45

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

#29 by Harvey P. Dale at Fri Oct 23 19:49:23 EDT 2020

STATUS

editing

approved

#28 by Harvey P. Dale at Fri Oct 23 19:49:19 EDT 2020

LINKS

Harvey P. Dale, <a href="/A162557/b162557.txt">Table of n, a(n) for n = 0..1000</a>

STATUS

approved

editing

#27 by Harvey P. Dale at Fri Oct 23 19:45:39 EDT 2020

STATUS

editing

approved

#26 by Harvey P. Dale at Fri Oct 23 19:45:36 EDT 2020

MATHEMATICA

LinearRecurrence[{8, -13}, {1, 5}, 30] (* Harvey P. Dale, Oct 23 2020 *)

STATUS

approved

editing

#25 by N. J. A. Sloane at Sat Nov 05 14:03:27 EDT 2016

STATUS

proposed

approved

#24 by Andrey Zabolotskiy at Thu Oct 27 06:50:44 EDT 2016

STATUS

editing

proposed

#23 by Andrey Zabolotskiy at Thu Oct 27 06:43:17 EDT 2016

LINKS

<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-13).

STATUS

proposed

editing

Discussion

Thu Oct 27

06:50

Andrey Zabolotskiy: Ilya, your comments about substitutional systems in this and other sequences look a bit odd. Of course, this is a nice illustration to the reduction of an order-2 linear recurrence to 2 connected order-1 linear recurrences, but a question arises immediately: why have these particular substitutions been chosen, why not, say, {0 -> 1110000, 1 -> 11110}?

#22 by Michel Marcus at Mon Oct 03 05:53:52 EDT 2016

STATUS

editing

proposed

#21 by Michel Marcus at Mon Oct 03 05:53:23 EDT 2016

COMMENTS

Binomial transform of A086405.

4th binomial transform of A108411.

Binomial transform of A086405. 2nd binomial transform of A079935. 4th binomial transform of A108411. [R. J. Mathar, Jul 17 2009]

STATUS

proposed

editing

Discussion

Mon Oct 03

05:53

Michel Marcus: The comments with  A108411 and A086405 were here before Richard comment.