A048592 - OEIS

%I #21 Jan 18 2025 15:29:21

%S 9,10,12,15,19,25,33,44,59,80,109,149,204,280,385,530,730,1006,1387,

%T 1913,2639,3641,5024,6933,9568,13205,18225,25154,34718,47919,66140,

%U 91290,126004,173919,240055,331341,457341,631256,871307,1202644,1659981,2291233,3162536

%N Pisot sequence L(9,10).

%H Colin Barker, <a href="/A048592/b048592.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = 2*a(n-1) - a(n-2) + a(n-4) - a(n-5) (holds at least up to n = 1000 but is not known to hold in general).

%t RecurrenceTable[{a[0] == 9, a[1] == 10, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 50}] (* _Bruno Berselli_, Feb 04 2016 *)

%t nxt[{a_,b_}]:={b,Ceiling[b^2/a]}; NestList[nxt,{9,10},50][[;;,1]] (* _Harvey P. Dale_, Jan 18 2025 *)

%o (Magma) Lxy:=[9, 10]; [n le 2 select Lxy[n] else Ceiling(Self(n-1)^2/Self(n-2)): n in [1..50]]; // _Bruno Berselli_, Feb 04 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, 9, 10) \\ _Colin Barker_, Aug 07 2016

%Y See A008776 for definitions of Pisot sequences.

%K nonn,changed

%O 0,1

%A _David W. Wilson_