A048585 Pisot sequence L(6,7).

6, 7, 9, 12, 16, 22, 31, 44, 63, 91, 132, 192, 280, 409, 598, 875, 1281, 1876, 2748, 4026, 5899, 8644, 12667, 18563, 27204, 39868, 58428, 85629, 125494, 183919, 269545, 395036, 578952, 848494, 1243527, 1822476, 2670967, 3914491, 5736964, 8407928, 12322416, 18059377

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for Pisot sequences

Crossrefs

See A008776 for definitions of Pisot sequences.

Programs

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

Maple

L := proc(a0,a1,n)
    option remember;
    if n = 0 then
        a0 ;
    elif n = 1 then
        a1;
    else
        ceil( procname(a0,a1,n-1)^2/procname(a0,a1,n-2)) ;
    end if;
end proc:
A048585 := proc(n)
    L(6,7,n) ;
end proc:

Mathematica

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 *)

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

Formula

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).