A018910 Pisot sequence L(4,5).

4, 5, 7, 10, 15, 23, 36, 57, 91, 146, 235, 379, 612, 989, 1599, 2586, 4183, 6767, 10948, 17713, 28659, 46370, 75027, 121395, 196420, 317813, 514231, 832042, 1346271, 2178311, 3524580, 5702889, 9227467, 14930354, 24157819, 39088171, 63245988, 102334157, 165580143

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 linear recurrences with constant coefficients, signature (2, 0, -1).

Index entries for Pisot sequences

Formula

a(n) = Fib(n+3)+2 = A020743(n-2) = A157725(n+3); a(n) = 2a(n-1) - a(n-3).

G.f.: -(-4+3*x+3*x^2)/(x-1)/(x^2+x-1) = -2/(x-1)+(-x-2)/(x^2+x-1) . - R. J. Mathar, Nov 23 2007

Mathematica

LinearRecurrence[{2, 0, -1}, {4, 5, 7}, 40] (* Jean-François Alcover, Dec 12 2016 *)

Prog

(PARI) pisotL(nmax, a1, a2) = {
  a=vector(nmax); a[1]=a1; a[2]=a2;
  for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]));
  a
}
pisotL(50, 4, 5) \\ Colin Barker, Aug 07 2016

Crossrefs

See A008776 for definitions of Pisot sequences.

Sequence in context: A093517 A248858 A145018 * A022936 A057708 A032686

Adjacent sequences: A018907 A018908 A018909 * A018911 A018912 A018913

Keyword

nonn,easy

Author

R. K. Guy

Status

approved