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%I #15 Jan 31 2023 17:08:59
%S 9,15,25,42,71,120,203,343,580,981,1659,2806,4746,8027,13576,22961,
%T 38834,65680,111085,187879,317761,537431,908960,1537329,2600093,
%U 4397552,7437605,12579264,21275381,35983173,60858545,102930403,174086776,294433954,497977820
%N Pisot sequence E(9,15), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).
%H Colin Barker, <a href="/A014003/b014003.txt">Table of n, a(n) for n = 0..1000</a>
%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="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>, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.
%F Known not to satisfy any linear recurrence.
%t nxt[{a_,b_}]:={b,Floor[b^2/a+1/2]}; NestList[nxt,{9,15},40][[All,1]] (* _Harvey P. Dale_, Jan 31 2023 *)
%o (PARI) pisotE(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]+1/2));
%o a
%o }
%o pisotE(50, 9, 15) \\ _Colin Barker_, Jul 28 2016
%K nonn
%O 0,1
%A _Simon Plouffe_
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