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

0,1

Links

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

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).

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 *)

Prog

(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
(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

Crossrefs

See A008776 for definitions of Pisot sequences.

Cf. A003411.

Sequence in context: A087668 A120176 A139049 * A168415 A199635 A131864

Adjacent sequences: A048587 A048588 A048589 * A048591 A048592 A048593

Keyword

nonn

Author

David W. Wilson

Status

approved