A048626 Pisot sequence P(6,9).

6, 9, 13, 19, 28, 41, 60, 88, 129, 189, 277, 406, 595, 872, 1278, 1873, 2745, 4023, 5896, 8641, 12664, 18560, 27201, 39865, 58425, 85626, 125491, 183916, 269542, 395033, 578949, 848491, 1243524, 1822473, 2670964, 3914488, 5736961, 8407925, 12322413, 18059374

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,1).

Crossrefs

Subsequence of A048625, A000930. See A008776 for definitions of Pisot sequences.

Cf. A020721.

Programs

Mathematica

LinearRecurrence[{1, 0, 1}, {6, 9, 13}, 42] (* Robert G. Wilson v, Jul 12 2014 *)

PARI

pisotP(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]-1/2));
  a
}
pisotP(50, 6, 9) \\ Colin Barker, Aug 08 2016

Formula

a(n) = a(n-1) + a(n-3) (Checked up to n = 1000)

a(n) = A048625(n+1). - R. J. Mathar, Oct 15 2008