A048588 Pisot sequence L(7,8).

7, 8, 10, 13, 17, 23, 32, 45, 64, 92, 133, 193, 281, 410, 599, 876, 1282, 1877, 2749, 4027, 5900, 8645, 12668, 18564, 27205, 39869, 58429, 85630, 125495, 183920, 269546, 395037, 578953, 848495, 1243528, 1822477, 2670968, 3914492, 5736965, 8407929, 12322417

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 = 72000 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:
A048588 := proc(n)
    L(7, 8, n) ;
end proc: # R. J. Mathar, Feb 12 2016

Mathematica

RecurrenceTable[{a[0] == 7, a[1] == 8, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 50}] (* Bruno Berselli, Feb 05 2016 *)

Prog

(Magma) Lxy:=[7, 8]; [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) pisotL(nmax, a1, a2) = {
  a=vector(nmax); a[1]=a1; a[2]=a2;
  for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]));
  a
}
pisotL(50, 7, 8) \\ Colin Barker, Aug 07 2016

Crossrefs

See A008776 for definitions of Pisot sequences.

Sequence in context: A067529 A080113 A243078 * A141676 A127164 A153972

Adjacent sequences: A048585 A048586 A048587 * A048589 A048590 A048591

Keyword

nonn

Author

David W. Wilson

Status

approved