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%I #37 Aug 31 2018 09:45:34
%S 7,9,12,16,21,28,37,49,65,86,114,151,200,265,351,465,616,816,1081,
%T 1432,1897,2513,3329,4410,5842,7739,10252,13581,17991,23833,31572,
%U 41824,55405,73396,97229,128801,170625,226030,299426,396655,525456,696081,922111,1221537
%N Pisot sequences E(7,9), P(7,9).
%H Colin Barker, <a href="/A020720/b020720.txt">Table of n, a(n) for n = 0..1000</a>
%H S. B. Ekhad, N. J. A. Sloane, D. Zeilberger, <a href="http://arxiv.org/abs/1609.05570">Automated proofs (or disproofs) of linear recurrences satisfied by Pisot Sequences</a>, arXiv:1609.05570 [math.NT] (2016)
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 1).
%F a(n) = a(n-2) + a(n-3) for n>=3. (Proved using the PtoRv program of Ekhad-Sloane-Zeilberger.) - N. J. A. Sloane, Sep 09 2016
%F G.f.: (7+9*x+5*x^2) / (1-x^2-x^3). - _Colin Barker_, Jun 05 2016
%t LinearRecurrence[{0, 1, 1}, {7, 9, 12}, 50] (* _Jean-François Alcover_, Aug 31 2018 *)
%t CoefficientList[Series[(7 + 9 x + 5 x^2)/(1 - x^2 - x^3), {x, 0, 50}], x] (* _Stefano Spezia_, Aug 31 2018 *)
%Y A subsequence of A000931.
%Y See A008776 for definitions of Pisot sequences.
%Y The following are basically all variants of the same sequence: A000931, A078027, A096231, A124745, A133034, A134816, A164001, A182097, A228361 and probably A020720. However, each one has its own special features and deserves its own entry.
%K nonn
%O 0,1
%A _David W. Wilson_
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