A020736 Pisot sequence L(5,8).

5, 8, 13, 22, 38, 66, 115, 201, 352, 617, 1082, 1898, 3330, 5843, 10253, 17992, 31573, 55406, 97230, 170626, 299427, 525457, 922112, 1618193, 2839730, 4983378, 8745218, 15346787, 26931733, 47261896, 82938845, 145547526, 255418102, 448227522, 786584467

Offset

0,1

Links

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

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - a(n-4) (holds at least up to n = 1000 but is not known to hold in general).

Mathematica

RecurrenceTable[{a[0] == 5, a[1] == 8, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 40}] (* Bruno Berselli, Feb 05 2016 *)

Prog

(Magma) Lxy:=[5, 8]; [n le 2 select Lxy[n] else Ceiling(Self(n-1)^2/Self(n-2)): n in [1..40]]; // 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, 5, 8) \\ Colin Barker, Aug 07 2016

Crossrefs

See A008776 for definitions of Pisot sequences.

Sequence in context: A314468 A111321 A306943 * A314469 A217185 A160421

Adjacent sequences: A020733 A020734 A020735 * A020737 A020738 A020739

Keyword

nonn

Author

David W. Wilson

Status

approved