A048590 Pisot sequence L(8,9).

8, 9, 11, 14, 18, 24, 32, 43, 58, 79, 108, 148, 203, 279, 384, 529, 729, 1005, 1386, 1912, 2638, 3640, 5023, 6932, 9567, 13204, 18224, 25153, 34717, 47918, 66139, 91289, 126003, 173918, 240054, 331340, 457340, 631255, 871306, 1202643, 1659980, 2291232, 3162535

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

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

Crossrefs

See A008776 for definitions of Pisot sequences.

Cf. A003411.

Programs

Magma

Lxy:=[8,9]; [n le 2 select Lxy[n] else Ceiling(Self(n-1)^2/Self(n-2)): n in [1..50]]; // Bruno Berselli, Feb 05 2016

Mathematica

RecurrenceTable[{a[0] == 8, a[1] == 9, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 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, 8, 9) \\ Colin Barker, Aug 07 2016

Formula

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