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Pisot sequences E(3,7), P(3,7).
(history; published version)
#72 by Charles R Greathouse IV at Thu Sep 08 08:44:37 EDT 2022
PROG

(MAGMAMagma) XY:=[3, 7]; [n le 2 select XY[n] else Ceiling(Self(n-1)^2/Self(n-2)-1/2): n in [1..32]]; // Klaus Brockhaus, Nov 17 2010

(MAGMAMagma) a:=1; b:=1; c:=1; S:=[]; for n in [1..32] do a+:=b; b+:=c; c+:=a; Append(~S, c); end for; S; // Klaus Brockhaus, Nov 17 2010

Discussion
Thu Sep 08
08:44
OEIS Server: https://oeis.org/edit/global/2944
#71 by N. J. A. Sloane at Sun Mar 28 21:22:25 EDT 2021
STATUS

editing

approved

#70 by N. J. A. Sloane at Sun Mar 28 21:22:23 EDT 2021
LINKS

Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, <a href="http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/pisot.html">Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences</a>, 2016; <a href="/A010912/a010912.pdf">Local copy</a> [pdf file only, no active links]

N. J. A. Sloane, <a href="/A010912/a010912.pdf">TITLE FOR LINK</a>

STATUS

approved

editing

#69 by N. J. A. Sloane at Sun Mar 28 21:20:31 EDT 2021
STATUS

editing

approved

#68 by N. J. A. Sloane at Sun Mar 28 21:20:29 EDT 2021
LINKS

N. J. A. Sloane, <a href="/A010912/a010912.pdf">TITLE FOR LINK</a>

STATUS

approved

editing

#67 by N. J. A. Sloane at Sun Mar 28 21:20:04 EDT 2021
STATUS

editing

approved

#66 by N. J. A. Sloane at Sun Mar 28 21:20:01 EDT 2021
LINKS

S. B. Ekhad, N. J. A. Sloane, D. Zeilberger, <a href="http://arxiv.org/abs/1609.05570">Automated proofs (or disproofs) of linear recurrences satisfied by Pisot Sequences</a>, arXiv:1609.05570 [math.NT] (2016). [This is a different document from the one with the same title on Doron Zeilberger's web site]

STATUS

approved

editing

#65 by Susanna Cuyler at Tue Mar 10 10:26:22 EDT 2020
STATUS

proposed

approved

#64 by Michel Marcus at Tue Mar 10 04:25:48 EDT 2020
STATUS

editing

proposed

#63 by Michel Marcus at Tue Mar 10 04:25:44 EDT 2020
LINKS

D. W. Boyd, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa32/aa32110.pdf">Pisot sequences which satisfy no linear recurrences</a>, Acta Arith. 32 (1) (1977) 89-98.

D. W. Boyd, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa34/aa3444.pdf">Some integer sequences related to the Pisot sequences</a>, Acta Arithmetica, 34 (1979), 295-305.

D. W. Boyd, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa47/aa4712.pdf">On linear recurrence relations satisfied by Pisot sequences</a>, Acta Arithm. 47 (1) (1986) 13.

D. W. Boyd, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa48/aa4825.pdf">Pisot sequences which satisfy no linear recurrences. II</a>, Acta Arithm. 48 (1987) 191.

STATUS

proposed

editing