A019492 Pisot sequence T(4,9), a(n) = floor(a(n-1)^2/a(n-2)).

4, 9, 20, 44, 96, 209, 455, 990, 2154, 4686, 10194, 22176, 48241, 104942, 228287, 496607, 1080300, 2350043, 5112193, 11120867, 24191904, 52626132, 114480851, 249037213, 541745915, 1178493097, 2563648273, 5576861234, 12131688091, 26390804748, 57409535261

Offset

0,1

Comments

Satisfies the linear recurrence a(n) = 3*a(n-1) - 4*a(n-3) + a(n-6) just for n <= 10 (see A019493).

Links

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

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.

Index entries for Pisot sequences

Mathematica

RecurrenceTable[{a[0] == 4, a[1] == 9, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 40}] (* Bruno Berselli, Feb 04 2016 *)
nxt[{a_, b_}]:={b, Floor[b^2/a]}; NestList[nxt, {4, 9}, 40][[All, 1]] (* Harvey P. Dale, Aug 22 2017 *)

Prog

(Magma) Iv:=[4, 9]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..40]]; // Bruno Berselli, Feb 04 2016
(PARI) pisotT(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]));
  a
}
pisotT(50, 4, 9) \\ Colin Barker, Jul 29 2016

Crossrefs

See A008776 for definitions of Pisot sequences.

Cf. A019493.

Sequence in context: A133095 A132175 A019493 * A020708 A345192 A109110

Adjacent sequences: A019489 A019490 A019491 * A019493 A019494 A019495

Keyword

nonn

Author

R. K. Guy

Status

approved