A014008 Pisot sequence E(10,22), a(n) = floor( a(n-1)^2/a(n-2)+1/2 ).

10, 22, 48, 105, 230, 504, 1104, 2418, 5296, 11600, 25408, 55652, 121896, 266992, 584800, 1280904, 2805600, 6145184, 13459968, 29481744, 64574688, 141439744, 309799425, 678562341, 1486274065, 3255427634, 7130454154, 15618033069, 34208614441, 74928084529

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.

a(n) = floor(r*s^n+1/2), where r = 9.99722327450628273875296... and s = 2.190327955501779639125414331914733218563545664874673678481473094... . - Benoit Cloitre, Apr 21 2003

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, 10, 22) \\ Colin Barker, Jul 29 2016

Crossrefs

Sequence in context: A179877 A216048 A079861 * A219744 A246419 A039315

Adjacent sequences: A014005 A014006 A014007 * A014009 A014010 A014011

Keyword

nonn

Author

Simon Plouffe

Status

approved