A020728 Pisot sequence T(2,9), a(n) = floor(a(n-1)^2/a(n-2)).

2, 9, 40, 177, 783, 3463, 15315, 67730, 299533, 1324671, 5858296, 25908042, 114577112, 506711954, 2240910072, 9910320668, 43827932664, 193826995709, 857190882207, 3790886846546, 16765020932461, 74142526074589, 327891876477017, 1450086587978657

Offset

0,1

Links

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

Formula

Pisot sequence T(x, y): a(0) = x, a(1) = y, a(n) = floor(a(n-1)^2/a(n-2)).

Mathematica

RecurrenceTable[{a[0] == 2, a[1] == 9, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 30}] (* Bruno Berselli, Feb 04 2016 *)

Prog

(PARI) lista(nn) = {print1(x = 2, ", ", y = 9, ", "); for (n=1, nn, z = y^2\x; print1(z, ", "); x = y; y = z; ); } \\ Michel Marcus, Feb 04 2016
(Magma) Iv:=[2, 9]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..30]]; // Bruno Berselli, Feb 04 2016
(PARI) pisotT(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]));
  a
}
pisotT(50, 2, 9) \\ Colin Barker, Jul 29 2016

Crossrefs

See A008776 for definitions of Pisot sequences.

Sequence in context: A019066 A097070 A164033 * A107979 A021001 A231134

Adjacent sequences: A020725 A020726 A020727 * A020729 A020730 A020731

Keyword

nonn

Author

David W. Wilson

Status

approved