A014001 Pisot sequence E(7,15), a(n)=[ a(n-1)^2/a(n-2)+1/2 ].

7, 15, 32, 68, 145, 309, 658, 1401, 2983, 6351, 13522, 28790, 61297, 130508, 277866, 591608, 1259600, 2681830, 5709918, 12157058, 25883745, 55109407, 117334132, 249817577, 531889747, 1132453154, 2411120262, 5133546494, 10929898447, 23270984338, 49546545623

Offset

0,1

Links

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

D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305.

D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.

Index entries for Pisot sequences

Formula

Known not to satisfy any linear recurrence.

There are linear recurrences which match e.g. the first 21 terms, but after a while they always fail. - N. J. A. Sloane, Aug 07 2016

Maple

PisotE := proc(a0, a1, n)
    option remember;
    if n = 0 then
        a0 ;
    elif n = 1 then
        a1;
    else
        floor( procname(a0, a1, n-1)^2/procname(a0, a1, n-2)+1/2) ;
    end if;
end proc:
A014001 := proc(n)
    PisotE(7, 15, n) ;
end proc: # R. J. Mathar, Feb 12 2016

Mathematica

a[0] = 7; a[1] = 15;
a[n_] := a[n] = Floor[a[n-1]^2/a[n-2] + 1/2];
a /@ Range[0, 30] (* Jean-François Alcover, Apr 03 2020 *)

Prog

(PARI) pisotE(nmax, a1, a2) = {
  a=vector(nmax); a[1]=a1; a[2]=a2;
  for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]+1/2));
  a
}
pisotE(50, 7, 15) \\ Colin Barker, Jul 27 2016

Crossrefs

Sequence in context: A078485 A233297 A159695 * A291642 A271995 A174792

Adjacent sequences: A013998 A013999 A014000 * A014002 A014003 A014004

Keyword

nonn

Author

Simon Plouffe, Dec 11 1996

Status

approved