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

0,1

Links

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

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

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 *)

Prog

(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

Crossrefs

See A008776 for definitions of Pisot sequences.

Sequence in context: A122498 A132750 A297296 * A069231 A243635 A243636

Adjacent sequences: A048579 A048580 A048581 * A048583 A048584 A048585

Keyword

nonn

Author

David W. Wilson

Status

approved