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

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for Pisot sequences

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).

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 *)

Prog

(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
(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

Crossrefs

See A008776 for definitions of Pisot sequences.

Sequence in context: A108595 A186079 A022938 * A169761 A049304 A168614

Adjacent sequences: A048582 A048583 A048584 * A048586 A048587 A048588

Keyword

nonn

Author

David W. Wilson

Status

approved