A048625 Pisot sequence P(4,6).

4, 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

0,1

Comments

Conjecture: satisfies a linear recurrence having signature (1, 0, 1). - Harvey P. Dale, Jun 05 2021

Links

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

Index entries for Pisot sequences

Formula

a(n) = a(n-1) + a(n-3) (Checked up to n = 48000).

G.f.: (conjecture) (( Q(0)-1)/2 -(x+x^2+x^3+2*x^4+3*x^5))/x^6, where Q(k) = 1 + x^3 + (2*k+3)*x - x*(2*k+1 + x^2)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 05 2013

Maple

P := proc(a0, a1, n)
    option remember;
    if n = 0 then
        a0 ;
    elif n = 1 then
        a1;
    else
        ceil( procname(a0, a1, n-1)^2/procname(a0, a1, n-2)-1/2) ;
    end if;
end proc:
A048625 := proc(n)
    P(4, 6, n) ;
end proc: # R. J. Mathar, Feb 12 2016

Mathematica

P[a0_, a1_, n_] := P[a0, a1, n] = Switch[n, 0, a0, 1, a1, _, Ceiling[P[a0, a1, n-1]^2/P[a0, a1, n-2] - 1/2]];
a[n_] := P[4, 6, n];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Oct 25 2023, after R. J. Mathar *)

Prog

(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, 4, 6) \\ Colin Barker, Aug 08 2016

Crossrefs

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

Sequence in context: A283623 A020747 A010737 * A120134 A241451 A354965

Adjacent sequences: A048622 A048623 A048624 * A048626 A048627 A048628

Keyword

nonn

Author

David W. Wilson

Status

approved