cp's OEIS Frontend

A048585 Pisot sequence L(6,7).

%I A048585 #18 Sep 08 2022 08:44:57
%S A048585 6,7,9,12,16,22,31,44,63,91,132,192,280,409,598,875,1281,1876,2748,
%T A048585 4026,5899,8644,12667,18563,27204,39868,58428,85629,125494,183919,
%U A048585 269545,395036,578952,848494,1243527,1822476,2670967,3914491,5736964,8407928,12322416,18059377
%N A048585 Pisot sequence L(6,7).
%H A048585 Colin Barker, <a href="/A048585/b048585.txt">Table of n, a(n) for n = 0..1000</a>
%H A048585 <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>
%F A048585 a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) (holds at least up to n = 50000 but is not known to hold in general).
%p A048585 L := proc(a0,a1,n)
%p A048585     option remember;
%p A048585     if n = 0 then
%p A048585         a0 ;
%p A048585     elif n = 1 then
%p A048585         a1;
%p A048585     else
%p A048585         ceil( procname(a0,a1,n-1)^2/procname(a0,a1,n-2)) ;
%p A048585     end if;
%p A048585 end proc:
%p A048585 A048585 := proc(n)
%p A048585     L(6,7,n) ;
%p A048585 end proc:
%t A048585 RecurrenceTable[{a[0] == 6, a[1] == 7, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 50}] (* _Bruno Berselli_, Feb 05 2016 *)
%o A048585 (Magma) Lxy:=[6,7]; [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 A048585 (PARI) first(n)=my(v=vector(n+1)); v[1]=6; v[2]=7; for(i=3,#v,v[i]=ceil(v[i-1]^2/v[i-2])); v \\ _Charles R Greathouse IV_, Feb 12 2016
%Y A048585 See A008776 for definitions of Pisot sequences.
%K A048585 nonn
%O A048585 0,1
%A A048585 _David W. Wilson_