A020748 Pisot sequence T(4,10), a(n) = floor(a(n-1)^2/a(n-2)).

4, 10, 25, 62, 153, 377, 928, 2284, 5621, 13833, 34042, 83774, 206159, 507335, 1248496, 3072412, 7560869, 18606469, 45788478, 112680418, 277294139, 682390435, 1679287948, 4132543288, 10169735361, 25026602289, 61587720810, 151560619806, 372974046999

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

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

Crossrefs

See A008776 for definitions of Pisot sequences.

Programs

Mathematica

RecurrenceTable[{a[0]==4,a[1]==10,a[n]==Floor[a[n-1]^2/a[n-2]]},a,{n,30}] (* Harvey P. Dale, Dec 26 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, 4, 10) \\ Colin Barker, Jul 29 2016

Formula

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

Note the warning in A010925 from Pab Ter (pabrlos(AT)yahoo.com), May 23 2004: [A010925] and other examples show that it is essential to reject conjectured generating functions for Pisot sequences until a proof or reference is provided. - N. J. A. Sloane, Jul 26 2016