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Pisot sequence T(3,5).
4

%I #24 Sep 08 2022 08:44:45

%S 3,5,8,12,18,27,40,59,87,128,188,276,405,594,871,1277,1872,2744,4022,

%T 5895,8640,12663,18559,27200,39864,58424,85625,125490,183915,269541,

%U 395032,578948,848490,1243523,1822472,2670963,3914487,5736960,8407924,12322412,18059373

%N Pisot sequence T(3,5).

%H Vincenzo Librandi, <a href="/A020745/b020745.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=877">Encyclopedia of Combinatorial Structures 877</a>

%F a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) (holds at least up to n = 1000 but is not known to hold in general).

%F Empirical g.f.: (3-x+x^2-2*x^3)/(1-x)/(1-x-x^3). [_Colin Barker_, Feb 19 2012]

%t RecurrenceTable[{a[0] == 3, a[1] == 5, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 50}] (* _Bruno Berselli_, Feb 04 2016 *)

%o (Magma) Iv:=[3,5]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..50]]; // _Bruno Berselli_, Feb 04 2016

%Y See A008776 for definitions of Pisot sequences.

%K nonn,easy

%O 0,1

%A _David W. Wilson_