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%I #26 Dec 30 2023 23:43:37
%S 4,6,9,14,22,35,56,90,145,234,378,611,988,1598,2585,4182,6766,10947,
%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(4,6), E(4,6).
%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 Vincenzo Librandi, <a href="/A020706/b020706.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1).
%F a(n) = Fib(n+4)+1 = A000045(n+4)+1.
%F a(n) = 2a(n-1) - a(n-3).
%F G.f.: (4-2*x-3*x^2)/(1-x)/(1-x-x^2). - _Colin Barker_, Feb 21 2012
%t CoefficientList[Series[(4-2*x-3*x^2)/(1-x)/(1-x-x^2),{x,0,40}],x](* _Vincenzo Librandi_, Apr 20 2012 *)
%o (Magma) I:=[4, 6, 9]; [n le 3 select I[n] else 2*Self(n-1)-Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Apr 20 2012
%Y Subsequence of A001611, A048577. See A008776 for definitions of Pisot sequences.
%K nonn,easy
%O 0,1
%A _David W. Wilson_
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