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Pisot sequence E(9,19), a(n)=[ a(n-1)^2/a(n-2)+1/2 ].
1

%I #11 Jul 28 2016 13:05:41

%S 9,19,40,84,176,369,774,1624,3407,7148,14997,31465,66016,138507,

%T 290599,609700,1279199,2683861,5630953,11814185,24787095,52005287,

%U 109111208,228923950,480300565,1007708598,2114252392,4435868847,9306803910,19526411174,40967956027

%N Pisot sequence E(9,19), a(n)=[ a(n-1)^2/a(n-2)+1/2 ].

%H Colin Barker, <a href="/A014005/b014005.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.

%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, 19) \\ _Colin Barker_, Jul 28 2016

%K nonn

%O 0,1

%A _Simon Plouffe_