A048586 Pisot sequence L(6,8).

6, 8, 11, 16, 24, 36, 54, 81, 122, 184, 278, 421, 638, 967, 1466, 2223, 3371, 5112, 7753, 11759, 17835, 27051, 41030, 62233, 94394, 143176, 217169, 329402, 499638, 757853, 1149515, 1743590, 2644686, 4011473, 6084623, 9229188, 13998881, 21233577, 32207203

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for Pisot sequences

Crossrefs

Subsequence of A048583. See A008776 for definitions of Pisot sequences.

Programs

Maple

L := 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)) ;
    end if;
end proc:
A048586 := proc(n)
    L(6,8,n) ;
end proc: # R. J. Mathar, Feb 12 2016

Mathematica

L[a0_, a1_, n_] := L[a0, a1, n] = Switch[n, 0, a0, 1, a1, _, Ceiling[L[a0, a1, n-1]^2/L[a0, a1, n-2]]];
a[n_] := L[6, 8, n];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Oct 25 2023, after R. J. Mathar *)

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, 6, 8) \\ Colin Barker, Aug 07 2016