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 A020717 Pisot sequences L(6,9), E(6,9). 3
 6, 9, 14, 22, 35, 56, 90, 145, 234, 378, 611, 988, 1598, 2585, 4182, 6766, 10947, 17712, 28658, 46369, 75026, 121394, 196419, 317812, 514230, 832041, 1346270, 2178310, 3524579, 5702888, 9227466, 14930353, 24157818, 39088170, 63245987, 102334156, 165580142 (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 Index entries for linear recurrences with constant coefficients, signature (2,0,-1). FORMULA a(n) = Fibonacci(n+5)+1 = A001611(n+5). a(n) = 2*a(n-1) - a(n-3). a(n) = 1 + (5/2)*(1/2 + (1/2)*sqrt(5))^n + (11/10)*(1/2 +(1/2)*sqrt(5))^n*sqrt(5) - (11/10)*sqrt(5)*(1/2 - (1/2)*sqrt(5))^n + (5/2)*(1/2 - (1/2)*sqrt(5))^n. - Paolo P. Lava, Jun 10 2008 a(n) = A020706(n+1). - R. J. Mathar, Oct 25 2008 MATHEMATICA Table[Fibonacci[n + 5] + 1, {n, 0, 36}] (* Michael De Vlieger, Jul 27 2016 *) PROG (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, 6, 9) \\ Colin Barker, Jul 27 2016 CROSSREFS Subsequence of A001611, A048577. See A008776 for definitions of Pisot sequences. Pairwise sums of A018910. Sequence in context: A316019 A316020 A300573 * A196993 A303162 A242042 Adjacent sequences:  A020714 A020715 A020716 * A020718 A020719 A020720 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified January 18 16:27 EST 2020. Contains 331011 sequences. (Running on oeis4.)