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A048575 Pisot sequences L(2,5), E(2,5). 1
2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229, 1346269, 3524578, 9227465, 24157817, 63245986, 165580141, 433494437, 1134903170, 2971215073, 7778742049, 20365011074, 53316291173, 139583862445, 365435296162, 956722026041 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, Preprint, 2016.

LINKS

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

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (3,-1)

FORMULA

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

G.f.: (2-x)/(1-3x+x^2). [Philippe Deléham, Nov 16 2008]

a(n) = [(3/2)+(1/2)*sqrt(5)]^n+(2/5)*[(3/2)+(1/2)*sqrt(5)]^n*sqrt(5)-(2/5)*[(3/2)-(1/2)*sqrt(5)]^n *sqrt(5)+[(3/2)-(1/2)*sqrt(5)]^n, with n>=0. [Paolo P. Lava, Nov 20 2008]

MATHEMATICA

LinearRecurrence[{3, -1}, {2, 5}, 40] (* Vincenzo Librandi, Jul 12 2015 *)

PROG

(MAGMA) [Fibonacci(2*n+3): n in [0..40]]; // Vincenzo Librandi, Jul 12 2015

(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, 2, 5) \\ Colin Barker, Jul 27 2016

CROSSREFS

Subsequence of A001519. See A008776 for definitions of Pisot sequences.

Sequence in context: A001519 * A099496 A122367 A114299 A112842 A097417

Adjacent sequences:  A048572 A048573 A048574 * A048576 A048577 A048578

KEYWORD

nonn,easy

AUTHOR

David W. Wilson

STATUS

approved

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Last modified September 22 00:25 EDT 2017. Contains 292326 sequences.