A021008 Pisot sequence P(5,11), a(0)=5, a(1)=11, a(n+1) is the nearest integer to a(n)^2/a(n-1).

5, 11, 24, 52, 113, 246, 536, 1168, 2545, 5545, 12081, 26321, 57346, 124941, 272212, 593075, 1292147, 2815232, 6133614, 13363453, 29115278, 63434160, 138205538, 301111747, 656039443, 1429328995, 3114113637, 6784794668

Offset

0,1

Links

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

J.-L. Baril, Classical sequences revisited with permutations avoiding dotted pattern, Electronic Journal of Combinatorics, 18 (2011), #P178.

Index entries for Pisot sequences

Formula

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

Conjecture: a(0)=5, a(1)=11, a(2)=24, a(3)=52, a(n)=3*a(n-1)-2*a(n-2)+a(n-4). - Harvey P. Dale, May 19 2015

Mathematica

nxt[{a_, b_}]:={b, Round[b^2/a]}; Transpose[NestList[nxt, {5, 11}, 30]][[1]] (* Harvey P. Dale, May 19 2015 *)
RecurrenceTable[{a[n] == Ceiling[a[n - 1]^2/a[n - 2] - 1/2], a[0] == 5, a[1] == 11}, a, {n, 0, 27}] (* Michael De Vlieger, Aug 08 2016 *)

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

Crossrefs

Sequence in context: A335153 A122926 A122925 * A266905 A059358 A296911

Adjacent sequences: A021005 A021006 A021007 * A021009 A021010 A021011

Keyword

nonn

Author

R. K. Guy

Status

approved