A048582 Pisot sequence L(4,9).

4, 9, 21, 49, 115, 270, 634, 1489, 3498, 8218, 19307, 45359, 106565, 250361, 588192, 1381884, 3246565, 7627402, 17919636, 42099965, 98908653, 232373629, 545933059, 1282602102, 3013314774, 7079409829, 16632196530, 39075285666, 91802543767, 215678705823

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.

Programs

Mathematica

a[n_] := a[n] = Switch[n, 0, 4, 1, 9, _, Ceiling[a[n-1]^2/a[n-2]]];
a /@ Range[0, 29] (* Jean-François Alcover, Oct 22 2019 *)

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, 4, 9) \\ Colin Barker, Aug 07 2016

Formula

a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) + a(n-4) - 2*a(n-5) + a(n-6) - a(n-7) (conjectured). Recurrence is satisfied for at least 760000 terms. - Chai Wah Wu, Jul 25 2016

Note the warning in A010925 from Pab Ter (pabrlos(AT)yahoo.com), May 23 2004: [A010925] and other examples show that it is essential to reject conjectured generating functions for Pisot sequences until a proof or reference is provided. - N. J. A. Sloane, Jul 26 2016