A276396 Pisot sequence E(30,989), a(n) = floor(a(n-1)^2/a(n-2) + 1/2).

30, 989, 32604, 1074844, 35433984, 1168139025, 38509606533, 1269531933775, 41852188998435, 1379725611747520, 45484903162012677, 1499483953941604826, 49432932068022376719, 1629637160449986379665, 53723644615396971780840, 1771087491625747409656874, 58386785286979621920361203, 1924815522816772987855854836

Offset

0,1

Comments

Satisfies a(n) = 33 a(n - 1) - 2 a(n - 2) + 30 a(n - 3) - 11 a(n - 4) for 4 <= n <= 15888 but not for n = 15889. It is not known if there is a linear recurrence which is valid for all n.

Links

Colin Barker, Table of n, a(n) for n = 0..650

S. B. Ekhad, N. J. A. Sloane, D. Zeilberger, Automated proofs (or disproofs) of linear recurrences satisfied by Pisot Sequences, arXiv:1609.05570 [math.NT] (2016)

Mathematica

a[0] = 30; a[1] = 989; a[n_] := a[n] = Floor[a[n-1]^2/a[n-2] + 1/2];
Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Oct 10 2018 *)

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(20, 30, 989) \\ Colin Barker, Sep 11 2016

Crossrefs

For definition of Pisot sequences see A008776.

Sequence in context: A111216 A158672 A268948 * A291070 A004994 A273626

Adjacent sequences: A276393 A276394 A276395 * A276397 A276398 A276399

Keyword

nonn

Author

N. J. A. Sloane, Sep 10 2016

Status

approved