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
Mohammad K. Azarian, Fibonacci Identities as Binomial Sums, International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 38, 2012, pp. 1871-1876 (See Corollary 1 (ix)).
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved