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A020695 Pisot sequence E(2,3). 5
2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Pisano period lengths: A001175. - R. J. Mathar, Aug 10 2012

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 (x)).

Tanya Khovanova, Recursive Sequences

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

FORMULA

a(n) = Fibonacci(n+3); a(n) = a(n-1) + a(n-2).

G.f.: (2+x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008

a(n) = (2^(-n)*((1-sqrt(5))^n*(-2+sqrt(5))+(1+sqrt(5))^n*(2+sqrt(5))))/sqrt(5). - Colin Barker, Jun 05 2016

E.g.f.: 2*(2*sqrt(5)*sinh(sqrt(5)*x/2) + 5*cosh(sqrt(5)*x/2))*exp(x/2)/5. - Ilya Gutkovskiy, Jun 05 2016

MATHEMATICA

CoefficientList[Series[(-x - 2)/(x^2 + x - 1), {x, 0, 200}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)

LinearRecurrence[{1, 1}, {2, 3}, 40] (* or *) Fibonacci[Range[3, 50]] (* Harvey P. Dale, Nov 22 2012 *)

PROG

(MAGMA) [Fibonacci(n+3): n in [0..50]]; // Vincenzo Librandi, Apr 23 2011

(PARI) a(n)=fibonacci(n+3) \\ Charles R Greathouse IV, Jan 17 2012

(PARI) Vec((2+x)/(1-x-x^2) + O(x^40)) \\ Colin Barker, Jun 05 2016

(GAP)

A020695:=List([0..10^3], n->Fibonacci(n+3)); # Muniru A Asiru, Sep 05 2017

CROSSREFS

Subsequence of A000045. See A008776 for definitions of Pisot sequences.

See A000045 for the Fibonacci numbers.

Sequence in context: A039834 A000045 A236191 * A212804 A132916 A274163

Adjacent sequences:  A020692 A020693 A020694 * A020696 A020697 A020698

KEYWORD

nonn,easy

AUTHOR

David W. Wilson

STATUS

approved

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Last modified September 23 22:42 EDT 2017. Contains 292395 sequences.