%I #27 Sep 08 2022 08:44:45

%S 3,7,16,36,81,182,408,914,2047,4584,10265,22986,51471,115255,258081,

%T 577899,1294040,2897633,6488421,14528964,32533461,72849384,163125366,

%U 365272615,817923579,1831505986,4101133972,9183316890,20563412382,46045882316,103106587509

%N Pisot sequence T(3,7), a(n) = floor(a(n-1)^2/a(n-2)).

%H Colin Barker, <a href="/A020746/b020746.txt">Table of n, a(n) for n = 0..1000</a>

%H D. W. Boyd, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa32/aa32110.pdf">Pisot sequences which satisfy no linear recurrences</a>, Acta Arith. 32 (1) (1977) 89-98

%H D. W. Boyd, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa34/aa3444.pdf">Some integer sequences related to the Pisot sequences</a>, Acta Arithmetica, 34 (1979), 295-305

%H D. W. Boyd, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa47/aa4712.pdf">On linear recurrence relations satisfied by Pisot sequences</a>, Acta Arithm. 47 (1) (1986) 13

%H D. W. Boyd, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa48/aa4825.pdf">Pisot sequences which satisfy no linear recurrences. II</a>, Acta Arithm. 48 (1987) 191

%H D. W. Boyd, <a href="https://www.researchgate.net/profile/David_Boyd7/publication/262181133_Linear_recurrence_relations_for_some_generalized_Pisot_sequences_-_annotated_with_corrections_and_additions/links/00b7d536d49781037f000000.pdf">Linear recurrence relations for some generalized Pisot sequences</a>, in Advances in Number Theory (Kingston ON, 1991), pp. 333-340, Oxford Univ. Press, New York, 1993; with updates from 1996 and 1999.

%H D. G. Cantor, <a href="http://www.numdam.org/item?id=ASENS_1976_4_9_2_283_0">On families of Pisot E-sequences</a>, Ann. Sci. Ecole Nat. Sup. 9 (2) (1976) 283-308

%F Conjectured g.f.: (-x^5+x^4-x^3+x^2-2*x+3)/((1-x)*(1-2*x-x^3-x^5)). - _Ralf Stephan_, May 12 2004

%F I believe that David Boyd has proved that this g.f. is correct. - _N. J. A. Sloane_, Aug 11 2016

%t RecurrenceTable[{a[0] == 3, a[1] == 7, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 40}] (* _Bruno Berselli_, Feb 04 2016 *)

%t nxt[{a_,b_}]:={b,Floor[b^2/a]}; NestList[nxt,{3,7},30][[All,1]] (* _Harvey P. Dale_, Oct 11 2020 *)

%o (Magma) Iv:=[3,7]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..40]]; // _Bruno Berselli_, Feb 04 2016

%o (PARI) pisotT(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]));

%o a

%o }

%o pisotT(50, 3, 7) \\ _Colin Barker_, Jul 29 2016

%Y See A008776 for definitions of Pisot sequences.

%Y Cf. A010919, A010925.

%K nonn

%O 0,1

%A _David W. Wilson_