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A020695
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Pisot sequence E(2,3).
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4
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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
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OFFSET
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0,1
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COMMENTS
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Pisano period lengths: A001175. - R. J. Mathar, Aug 10 2012
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LINKS
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Table of n, a(n) for n=0..38.
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).
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FORMULA
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a(n) = Fib(n+3); a(n) = a(n-1) + a(n-2).
G.f.: (2+x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Subsequence of A000045. See A008776 for definitions of Pisot sequences.
See A000045 for the Fibonacci numbers.
Sequence in context: A039834 A000045 A236191 * A212804 A132916 A177194
Adjacent sequences: A020692 A020693 A020694 * A020696 A020697 A020698
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KEYWORD
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nonn,easy
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AUTHOR
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David W. Wilson
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STATUS
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approved
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