login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

A020727
Pisot sequence P(2,7): a(0)=2, a(1)=7, thereafter a(n+1) is the nearest integer to a(n)^2/a(n-1).
5
2, 7, 24, 82, 280, 956, 3264, 11144, 38048, 129904, 443520, 1514272, 5170048, 17651648, 60266496, 205762688, 702517760, 2398545664, 8189147136, 27959497216, 95459694592, 325919783936, 1112759746560, 3799199418368, 12971278180352, 44286713884672
OFFSET
0,1
COMMENTS
Also Pisot sequence T(2,7). - R. K. Guy
It appears that a(n) = 4*a(n-1) - 2*a(n-2) (holds at least up to n = 1000 but is not known to hold in general).
The recurrence holds up to n = 10^5. - Ralf Stephan, Sep 03 2013
Empirical g.f.: (2-x)/(1-4*x+2*x^2). - Colin Barker, Feb 21 2012
LINKS
MATHEMATICA
RecurrenceTable[{a[0] == 2, a[1] == 7, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 30}] (* Bruno Berselli, Feb 04 2016 *)
PROG
(Magma) Iv:=[2, 7]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..30]]; // Bruno Berselli, Feb 04 2016
(PARI) pisotP(nmax, a1, a2) = {
a=vector(nmax); a[1]=a1; a[2]=a2;
for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]-1/2));
a
}
pisotP(50, 2, 7) \\ Colin Barker, Aug 08 2016
CROSSREFS
It appears that this is a subsequence of A003480.
See A008776 for definitions of Pisot sequences.
Sequence in context: A027128 A099463 A021000 * A003480 A378425 A329274
KEYWORD
nonn
EXTENSIONS
Edited by N. J. A. Sloane, Aug 17 2009 at the suggestion of R. J. Mathar.
STATUS
approved

pFad - Phonifier reborn

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.


Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy