login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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_