A010915 Pisot sequence E(6,16), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).

6, 16, 43, 116, 313, 845, 2281, 6157, 16619, 44858, 121081, 326823, 882164, 2381146, 6427213, 17348397, 46826965, 126395808, 341168818, 920886256, 2485665312, 6709332453, 18109896673, 48882412640, 131943892815, 356144263570, 961308127021, 2594772426806

Offset

0,1

Links

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

D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305.

D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.

Formula

Conjectured not to satisfy a linear recurrence.

Mathematica

RecurrenceTable[{a[1]==6, a[2]==16, a[n]==Floor[a[n-1]^2/a[n-2]+1/2]}, a[n], {n, 30}] (* Harvey P. Dale, Jun 26 2011 *)

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(50, 6, 16) \\ Colin Barker, Jul 28 2016

Crossrefs

Sequence in context: A263325 A107614 A317758 * A352115 A260384 A126360

Adjacent sequences: A010912 A010913 A010914 * A010916 A010917 A010918

Keyword

nonn

Author

Simon Plouffe

Status

approved