login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A020709 Pisot sequence E(4,10). 1
4, 10, 25, 63, 159, 401, 1011, 2549, 6427, 16205, 40859, 103021, 259755, 654941, 1651355, 4163693, 10498251, 26470077, 66741115, 168279693, 424297003, 1069813853, 2697406939, 6801187117, 17148375179, 43237565181, 109018319419, 274876578253, 693068226283 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

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

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = 3*a(n-1) - 2*a(n-2) + 2*a(n-3) (holds at least up to n = 1000 but is not known to hold in general).

Empirical g.f.: (4-2*x+3*x^2) / (1-3*x+2*x^2-2*x^3). - Colin Barker, Jun 05 2016

Theorem: a(n) = 3 a(n - 1) - 2 a(n - 2) + 2 a(n - 3) for n>=3. Proved using the PtoRv program of Ekhad-Sloane-Zeilberger, and implies the above conjectures. - N. J. A. Sloane, Sep 09 2016

MATHEMATICA

RecurrenceTable[{a[0] == 4, a[1] == 10, a[n] == Floor[a[n - 1]^2/a[n - 2] + 1/2]}, a, {n, 0, 40}] (* Bruno Berselli, Feb 05 2016 *)

PROG

(MAGMA) Exy:=[4, 10]; [n le 2 select Exy[n] else Floor(Self(n-1)^2/Self(n-2) + 1/2): n in [1..40]]; // Bruno Berselli, Feb 05 2016

CROSSREFS

See A008776 for definitions of Pisot sequences.

Sequence in context: A033539 A020748 A021004 * A020734 A225301 A298412

Adjacent sequences:  A020706 A020707 A020708 * A020710 A020711 A020712

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 19 18:30 EST 2019. Contains 320327 sequences. (Running on oeis4.)