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%I #31 Dec 30 2023 23:43:40
%S 6,9,14,22,35,56,90,145,234,378,611,988,1598,2585,4182,6766,10947,
%T 17712,28658,46369,75026,121394,196419,317812,514230,832041,1346270,
%U 2178310,3524579,5702888,9227466,14930353,24157818,39088170,63245987,102334156,165580142
%N Pisot sequences L(6,9), E(6,9).
%D Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, Preprint, 2016.
%H Colin Barker, <a href="/A020717/b020717.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1).
%F a(n) = Fibonacci(n+5)+1 = A001611(n+5).
%F a(n) = 2*a(n-1) - a(n-3).
%F a(n) = A020706(n+1). - _R. J. Mathar_, Oct 25 2008
%t Table[Fibonacci[n + 5] + 1, {n, 0, 36}] (* _Michael De Vlieger_, Jul 27 2016 *)
%o (PARI) pisotE(nmax, a1, a2) = {
%o a=vector(nmax); a[1]=a1; a[2]=a2;
%o for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]+1/2));
%o a
%o }
%o pisotE(50, 6, 9) \\ _Colin Barker_, Jul 27 2016
%Y Subsequence of A001611, A048577.
%Y See A008776 for definitions of Pisot sequences.
%Y Pairwise sums of A018910.
%K nonn,easy
%O 0,1
%A _David W. Wilson_
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