A021011 Pisot sequence P(6,11), a(0)=6, a(1)=11, a(n+1) is the nearest integer to a(n)^2/a(n-1).

6, 11, 20, 36, 65, 117, 211, 381, 688, 1242, 2242, 4047, 7305, 13186, 23802, 42965, 77556, 139996, 252706, 456158, 823408, 1486329, 2682964, 4843003, 8742077, 15780273, 28484880, 51417893, 92814143, 167538276, 302422379, 545900898

Offset

0,1

Links

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

Index entries for Pisot sequences

Formula

G.f.: (3x^5+2x^4+x^3+4x^2-x+6)/(-x^6-x^3+x^2-2x+1) (conjectured). - Ralf Stephan, May 12 2004

Mathematica

RecurrenceTable[{a[n] == Ceiling[a[n - 1]^2/a[n - 2] - 1/2], a[0] == 6, a[1] == 11}, a, {n, 0, 31}] (* or *)
First@ Transpose[NestList[{#2, Round[#2^2/#1]} & @@ # &, {6, 11}, 31]] (* Michael De Vlieger, Aug 08 2016, after Harvey P. Dale at A021008 *)

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, 6, 11) \\ Colin Barker, Aug 08 2016

Crossrefs

Sequence in context: A365351 A007745 A188556 * A000382 A208670 A208726

Adjacent sequences: A021008 A021009 A021010 * A021012 A021013 A021014

Keyword

nonn

Author

R. K. Guy

Status

approved