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 A010924 Pisot sequence E(8,55), a(n)=[ a(n-1)^2/a(n-2)+1/2 ]. 1
 8, 55, 378, 2598, 17856, 122724, 843480, 5797224, 39844224, 273848688, 1882157472, 12936036960, 88909166592, 611071221312, 4199882327424, 28865721292416, 198393621719040, 1363556058068736, 9371698078726656, 64411524820772352, 442699337396994048 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305. Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, Preprint, 2016. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.. Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5. S. B. Ekhad, N. J. A. Sloane, D. Zeilberger, Automated proofs (or disproofs) of linear recurrences satisfied by Pisot Sequences, arXiv:1609.05570 [math.NT] (2016) Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (6, 6). FORMULA Conjecture: a(n)=6*a(n-1)+6*a(n-2), n>1; a(0)=8, a(1)=55 . G.f.: (8+7x)/(1-6x-6x^2). - Philippe Deléham, Nov 19 2008 Theorem: a(n) = 6 a(n - 1) + 6 a(n - 2) for n>=2. Proved using the PtoRv program of Ekhad-Sloane-Zeilberger, and implies the above conjectures. - N. J. A. Sloane, Sep 09 2016 MATHEMATICA a[0] = 8; a[1] = 55; a[n_] := a[n] = Floor[a[n - 1]^2/a[n - 2] + 1/2]; Table[a[n], {n, 0, 20}] (* Michael De Vlieger, Jul 27 2016 *) PROG (PARI) pisotE(nmax, a1, a2) = {   a=vector(nmax); a[1]=a1; a[2]=a2;   for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]+1/2));   a } pisotE(50, 8, 55) \\ Colin Barker, Jul 27 2016 CROSSREFS Sequence in context: A143420 A075734 A033890 * A010918 A019484 A108984 Adjacent sequences:  A010921 A010922 A010923 * A010925 A010926 A010927 KEYWORD nonn,easy AUTHOR EXTENSIONS "Index entries..." based on conjectured formula deleted by Colin Barker, Jul 27 2016 STATUS approved

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Last modified November 19 11:04 EST 2017. Contains 294936 sequences.