A018914 Pisot sequence T(2,5), a(n) = floor(a(n-1)^2/a(n-2)).

2, 5, 12, 28, 65, 150, 346, 798, 1840, 4242, 9779, 22543, 51967, 119796, 276157, 636604, 1467515, 3382951, 7798460, 17977197, 41441465, 95531857, 220222323, 507661769, 1170274058, 2697743762, 6218903474, 14335965099, 33047609788, 76182140871, 175616894078

Offset

0,1

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

Formula

a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) - a(n-6) (holds at least up to n = 1000 but is not known to hold in general).

Mathematica

RecurrenceTable[{a[0] == 2, a[1] == 5, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 40}] (* Bruno Berselli, Feb 04 2016 *)

Prog

(Magma) Iv:=[2, 5]; [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
}

Crossrefs

See A008776 for definitions of Pisot sequences.

Sequence in context: A258898 A019486 A019485 * A129519 A034943 A181984

Adjacent sequences: A018911 A018912 A018913 * A018915 A018916 A018917

Keyword

nonn

Author

R. K. Guy

Status

approved