A014004 Pisot sequence E(9,17), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).

9, 17, 32, 60, 113, 213, 401, 755, 1422, 2678, 5043, 9497, 17885, 33682, 63432, 119459, 224972, 423680, 797898, 1502646, 2829867, 5329364, 10036557, 18901407, 35596190, 67036742, 126247353, 237756097, 447755619, 843238499, 1588034044, 2990674795, 5632206541

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

Known not to satisfy any linear recurrence.

Mathematica

nxt[{a_, b_}]:={b, Floor[b^2/a+1/2]}; NestList[nxt, {9, 17}, 40][[All, 1]] (* Harvey P. Dale, Sep 22 2017 *)

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, 9, 17) \\ Colin Barker, Jul 28 2016

Crossrefs

Sequence in context: A228260 A147459 A188559 * A090994 A164887 A328016

Adjacent sequences: A014001 A014002 A014003 * A014005 A014006 A014007

Keyword

nonn

Author

Simon Plouffe

Status

approved