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A048575
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Pisot sequences L(2,5), E(2,5).
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2
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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
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OFFSET
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0,1
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REFERENCES
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Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, Preprint, 2016.
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
Boothby, T.; Burkert, J.; Eichwald, M.; Ernst, D. C.; Green, R. M.; Macauley, M. On the cyclically fully commutative elements of Coxeter groups, J. Algebr. Comb. 36, No. 1, 123-148 (2012), Section 5.1
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (3,-1)
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FORMULA
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a(n) = A000045(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]
a(n) = 2*A001906(n+1)-A001906(n). - R. J. Mathar, Jun 11 2019
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MATHEMATICA
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LinearRecurrence[{3, -1}, {2, 5}, 40] (* Vincenzo Librandi, Jul 12 2015 *)
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PROG
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(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
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CROSSREFS
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Subsequence of A001519. See A008776 for definitions of Pisot sequences.
Sequence in context: A141448 A011783 A001519 * A099496 A122367 A114299
Adjacent sequences: A048572 A048573 A048574 * A048576 A048577 A048578
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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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