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A048575 Pisot sequences L(2,5), E(2,5). 2
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
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
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
FORMULA
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) = 2*A001906(n+1)-A001906(n). - R. J. Mathar, Jun 11 2019
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
Subsequence of A001519. See A008776 for definitions of Pisot sequences.
Sequence in context: A141448 A011783 A001519 * A099496 A122367 A367658
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified June 13 08:31 EDT 2024. Contains 373383 sequences. (Running on oeis4.)