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A020717 Pisot sequences L(6,9), E(6,9).

%I A020717 #35 Nov 01 2024 12:05:28
%S A020717 6,9,14,22,35,56,90,145,234,378,611,988,1598,2585,4182,6766,10947,
%T A020717 17712,28658,46369,75026,121394,196419,317812,514230,832041,1346270,
%U A020717 2178310,3524579,5702888,9227466,14930353,24157818,39088170,63245987,102334156,165580142
%N A020717 Pisot sequences L(6,9), E(6,9).
%D A020717 Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, Preprint, 2016.
%H A020717 Colin Barker, <a href="/A020717/b020717.txt">Table of n, a(n) for n = 0..1000</a>
%H A020717 Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, <a href="https://ceur-ws.org/Vol-3792/paper19.pdf">Integer sequences from k-iterated line digraphs</a>, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.
%H A020717 <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>
%H A020717 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1).
%F A020717 a(n) = Fibonacci(n+5)+1 = A001611(n+5).
%F A020717 a(n) = 2*a(n-1) - a(n-3).
%F A020717 a(n) = A020706(n+1). - _R. J. Mathar_, Oct 25 2008
%t A020717 Table[Fibonacci[n + 5] + 1, {n, 0, 36}] (* _Michael De Vlieger_, Jul 27 2016 *)
%o A020717 (PARI) pisotE(nmax, a1, a2) = {
%o A020717   a=vector(nmax); a[1]=a1; a[2]=a2;
%o A020717   for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]+1/2));
%o A020717   a
%o A020717 }
%o A020717 pisotE(50, 6, 9) \\ _Colin Barker_, Jul 27 2016
%Y A020717 Subsequence of A001611, A048577.
%Y A020717 See A008776 for definitions of Pisot sequences.
%Y A020717 Pairwise sums of A018910.
%K A020717 nonn,easy
%O A020717 0,1
%A A020717 _David W. Wilson_