The On-Line Encyclopedia of Integer Sequences (OEIS)

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A048575

Pisot sequences L(2,5), E(2,5).
(history; published version)

#39 by Joerg Arndt at Sat Dec 30 23:47:39 EST 2023

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editing

approved

#38 by Paolo P. Lava at Sat Dec 30 12:49:43 EST 2023

FORMULA

a(n) = [(3/2)+(1/2)*sqrt(5)]^n+(2/5)*[(3/2)+(1/2)*sqrt(5)]^n*sqrt(5)-(2/5)*[(3/2)-(1/2)*sqrt(5)]^n *sqrt(5)+[(3/2)-(1/2)*sqrt(5)]^n, with n>=0. [Paolo P. Lava, Nov 20 2008]

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#37 by Charles R Greathouse IV at Thu Sep 08 08:44:57 EDT 2022

PROG

(MAGMAMagma) [Fibonacci(2*n+3): n in [0..40]]; // Vincenzo Librandi, Jul 12 2015

Discussion

Thu Sep 08

08:44

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

#36 by R. J. Mathar at Tue Jun 11 07:57:41 EDT 2019

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#35 by R. J. Mathar at Tue Jun 11 07:57:23 EDT 2019

LINKS

Boothby, T.; Burkert, J.; Eichwald, M.; Ernst, D. C.; Green, R. M.; Macauley, M. <a href="https://doi.org/10.1007/s10801-011-0327-z">On the cyclically fully commutative elements of Coxeter groups</a>, J. Algebr. Comb. 36, No. 1, 123-148 (2012), Section 5.1

FORMULA

a(n) = FibA000045(2n+3). a(n) = 3a(n-1) - a(n-2).

a(n) = 2*A001906(n+1)-A001906(n). - R. J. Mathar, Jun 11 2019

STATUS

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editing

#34 by N. J. A. Sloane at Sat Sep 10 09:15:13 EDT 2016

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approved

#33 by N. J. A. Sloane at Sat Sep 10 09:15:11 EDT 2016

LINKS

Mohammad K. Azarian, <a href="http://www.m-hikari.com/ijcms/ijcms-2012/37-40-2012/azarianIJCMS37-40-2012.pdf">Fibonacci Identities as Binomial Sums</a>, International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 38, 2012, pp. 1871-1876 (See Corollary 1 (ix)).

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editing

#32 by N. J. A. Sloane at Sat Sep 10 09:14:13 EDT 2016

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approved

#31 by N. J. A. Sloane at Sat Sep 10 09:14:03 EDT 2016

REFERENCES

Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, Preprint, 2016.

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editing

#30 by Bruno Berselli at Wed Jul 27 06:02:34 EDT 2016

STATUS

reviewed

approved