The On-Line Encyclopedia of Integer Sequences® (OEIS®)

Revision History for A085449

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A085449

Horadam sequence (0,1,4,2).
(history; published version)

#40 by Ray Chandler at Thu Jun 29 18:21:55 EDT 2023

STATUS

editing

approved

#39 by Ray Chandler at Thu Jun 29 18:21:51 EDT 2023

LINKS

<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, 4).

STATUS

approved

editing

#38 by Charles R Greathouse IV at Thu Sep 08 08:45:11 EDT 2022

PROG

(MAGMAMagma) [2^(n-1)*Fibonacci(n): n in [0..50]]; // G. C. Greubel, Oct 08 2018

Discussion

Thu Sep 08

08:45

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

#37 by Michael Somos at Sun Mar 07 07:42:50 EST 2021

STATUS

editing

approved

#36 by Michael Somos at Sun Mar 07 07:42:38 EST 2021

FORMULA

a(n) = -(-4)^n*a(-n) for all integer n. - Michael Somos, Mar 07 2021

EXAMPLE

G.f. = x + 2*x^2 + 8*x^3 + 24*x^4 + 80*x^5 + 256*x^6 + 832*x^7 + ... - Michael Somos, Mar 07 2021

STATUS

approved

editing

Discussion

Sun Mar 07

07:42

Michael Somos: Added more info.

#35 by Joerg Arndt at Mon Feb 01 02:57:04 EST 2021

STATUS

reviewed

approved

#34 by Michel Marcus at Mon Feb 01 02:50:21 EST 2021

STATUS

proposed

reviewed

#33 by Amiram Eldar at Mon Feb 01 02:39:09 EST 2021

STATUS

editing

proposed

#32 by Amiram Eldar at Mon Feb 01 02:17:26 EST 2021

LINKS

F. P. Muga II, <a href="https://www.researchgate.net/publication/267327689">Extending the Golden Ratio and the Binet-de Moivre Formula</a>, March 2014; Preprint on ResearchGate, March 2014.

Eric Weisstein, <a href="http://mathworld.wolfram.com/HoradamSequence.html">Horadam Sequence</a>.

Eric Weisstein, <a href="http://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number</a>.

Eric Weisstein, <a href="http://mathworld.wolfram.com/PellNumber.html">Pell Number</a>.

Eric Weisstein, <a href="http://mathworld.wolfram.com/LucasNumber.html">Lucas Number</a>.

Eric Weisstein, <a href="http://mathworld.wolfram.com/LucasSequence.html">Lucas Sequence</a>.

#31 by Amiram Eldar at Mon Feb 01 02:16:06 EST 2021

FORMULA

Sum_{n>=1} 1/a(n) = A269991. - Amiram Eldar, Feb 01 2021

CROSSREFS

Cf. A024318, A000032, A000129, A001076, A085939, A269991.

STATUS

approved

editing