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Pisot sequence E(8,14), a(n)=[ a(n-1)^2/a(n-2)+1/2 ].
1

%I #12 Jun 28 2023 08:22:43

%S 8,14,25,45,81,146,263,474,854,1539,2773,4996,9001,16217,29218,52642,

%T 94845,170882,307878,554704,999411,1800640,3244215,5845106,10531134,

%U 18973956,34185398,61591870,110970141

%N Pisot sequence E(8,14), a(n)=[ a(n-1)^2/a(n-2)+1/2 ].

%H Harvey P. Dale, <a href="/A014002/b014002.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 RecurrenceTable[{a[0]==8,a[1]==14,a[n]==Floor[a[n-1]^2/a[n-2]+1/2]},a,{n,30}] (* _Harvey P. Dale_, Jan 31 2015 *)

%K nonn

%O 0,1

%A _Simon Plouffe_