A048591 - OEIS

%I #13 Sep 08 2022 08:44:57

%S 8,10,13,17,23,32,45,64,92,133,193,281,410,599,876,1282,1877,2749,

%T 4027,5900,8645,12668,18564,27205,39869,58429,85630,125495,183920,

%U 269546,395037,578953,848495,1243528,1822477,2670968,3914492,5736965,8407929,12322417,18059378

%N Pisot sequence L(8,10).

%H Colin Barker, <a href="/A048591/b048591.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) (holds at least up to n = 1000 but is not known to hold in general).

%t RecurrenceTable[{a[0] == 8, a[1] == 10, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 50}] (* _Bruno Berselli_, Feb 05 2016 *)

%o (Magma) Lxy:=[8,10]; [n le 2 select Lxy[n] else Ceiling(Self(n-1)^2/Self(n-2)): n in [1..50]]; // _Bruno Berselli_, Feb 05 2016

%o (PARI) pisotL(nmax, a1, a2) = {

%o   a=vector(nmax); a[1]=a1; a[2]=a2;

%o   for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]));

%o   a

%o }

%o pisotL(50, 8, 10) \\ _Colin Barker_, Aug 07 2016

%Y Subsequence of A048588.

%Y See A008776 for definitions of Pisot sequences.

%K nonn

%O 0,1

%A _David W. Wilson_