The On-Line Encyclopedia of Integer Sequences (OEIS)

A048575 revision #30

A048575

Pisot sequences L(2,5), E(2,5).

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

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));

}

pisotE(50, 2, 5) \\ Colin Barker, Jul 27 2016

CROSSREFS

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

Sequence in context: A141448 A011783 A001519 * A099496 A122367 A367658

Adjacent sequences: A048572 A048573 A048574 * A048576 A048577 A048578

KEYWORD

nonn,easy

AUTHOR

David W. Wilson

STATUS

approved