%I #18 Dec 30 2023 23:47:43

%S 3,4,6,9,14,22,35,56,90,145,234,378,611,988,1598,2585,4182,6766,10947,

%T 17712,28658,46369,75026,121394,196419,317812,514230,832041,1346270,

%U 2178310,3524579,5702888,9227466,14930353,24157818,39088170,63245987,102334156,165580142

%N Pisot sequence L(3,4).

%H Vincenzo Librandi, <a href="/A048577/b048577.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = Fib(n+3)+1. a(n) = 2a(n-1) - a(n-3).

%F a(n) = A020706(n-1), n>0. [From _R. J. Mathar_, Oct 15 2008]

%F G.f.: (3-2*x-2*x^2)/((1-x)*(1-x-x^2)). [_Colin Barker_, Apr 16 2012]

%t CoefficientList[Series[(3-2*x-2*x^2)/((1-x)*(1-x-x^2)),{x,0,40}],x] (* _Vincenzo Librandi_, Apr 27 2012 *)

%o (PARI) a(n)=fibonacci(n+3)+1 \\ _Charles R Greathouse IV_, Apr 16 2012

%o (Magma) [Fibonacci(n+3)+1: n in [0..40]]; // _Vincenzo Librandi_, Apr 27 2012

%Y Subsequence of A001611. See A008776 for definitions of Pisot sequences.

%K nonn,easy

%O 0,1

%A _David W. Wilson_