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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 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) 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 Adjacent sequences: A048572 A048573 A048574 * A048576 A048577 A048578 KEYWORD nonn,easy AUTHOR David W. Wilson STATUS approved

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