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Pisot sequence E(6,16), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).
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%I #22 Aug 06 2016 19:08:48

%S 6,16,43,116,313,845,2281,6157,16619,44858,121081,326823,882164,

%T 2381146,6427213,17348397,46826965,126395808,341168818,920886256,

%U 2485665312,6709332453,18109896673,48882412640,131943892815,356144263570,961308127021,2594772426806

%N Pisot sequence E(6,16), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).

%H Colin Barker, <a href="/A010915/b010915.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 Conjectured not to satisfy a linear recurrence.

%t RecurrenceTable[{a[1]==6,a[2]==16,a[n]==Floor[a[n-1]^2/a[n-2]+1/2]}, a[n],{n,30}] (* _Harvey P. Dale_, Jun 26 2011 *)

%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, 6, 16) \\ _Colin Barker_, Jul 28 2016

%K nonn

%O 0,1

%A _Simon Plouffe_