A014003 Pisot sequence E(9,15), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).

9, 15, 25, 42, 71, 120, 203, 343, 580, 981, 1659, 2806, 4746, 8027, 13576, 22961, 38834, 65680, 111085, 187879, 317761, 537431, 908960, 1537329, 2600093, 4397552, 7437605, 12579264, 21275381, 35983173, 60858545, 102930403, 174086776, 294433954, 497977820

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, 15}, 40][[All, 1]] (* Harvey P. Dale, Jan 31 2023 *)

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, 15) \\ Colin Barker, Jul 28 2016

Crossrefs

Sequence in context: A251415 A109888 A193227 * A333788 A082549 A013569

Adjacent sequences: A014000 A014001 A014002 * A014004 A014005 A014006

Keyword

nonn

Author

Simon Plouffe

Status

approved