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
Colin Barker, Table of n, a(n) for n = 0..1000
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Aug 17 2009 at the suggestion of R. J. Mathar.
STATUS
approved