login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A020716 Pisot sequences E(6,8), P(6,8). 1
6, 8, 11, 15, 20, 27, 36, 48, 64, 85, 113, 150, 199, 264, 350, 464, 615, 815, 1080, 1431, 1896, 2512, 3328, 4409, 5841, 7738, 10251, 13580, 17990, 23832, 31571, 41823, 55404, 73395, 97228, 128800, 170624, 226029, 299425, 396654, 525455, 696080, 922110, 1221536 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, arXiv:1609.05570 [math.NT], 2016.
FORMULA
a(n) = a(n-1) + a(n-2) - a(n-4) (holds at least up to n = 1000 but is not known to hold in general).
Empirical g.f.: (6+2*x-3*x^2-4*x^3) / ((1-x)*(1-x^2-x^3)). - Colin Barker, Jun 05 2016
Theorem: E(6,8) satisfies a(n) = a(n - 1) + a(n - 2) - a(n - 4) for n>=4. Proved using the PtoRv program of Ekhad-Sloane-Zeilberger. This shows that the above conjectures are correct. - N. J. A. Sloane, Sep 10 2016
a(n) = a(n-2) + a(n-3) + 1. - Greg Dresden, May 18 2020
MATHEMATICA
RecurrenceTable[{a[0]==6, a[1]==8, a[n]== Floor[a[n-1]^2/a[n-2] + 1/2]}, a, {n, 0, 50}] (* Bruno Berselli, Feb 05 2016 *)
PROG
(Magma) Exy:=[6, 8]; [n le 2 select Exy[n] else Floor(Self(n-1)^2/Self(n-2) + 1/2): n in [1..50]]; // Bruno Berselli, Feb 05 2016
(PARI) Vec((6+2*x-3*x^2-4*x^3)/((1-x)*(1-x^2-x^3)) + O(x^50)) \\ Jinyuan Wang, Mar 10 2020
CROSSREFS
This is a subsequence of A023434.
See A008776 for definitions of Pisot sequences.
Sequence in context: A287408 A287398 A167499 * A020937 A183208 A048586
KEYWORD
nonn
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)