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A010901 Pisot sequences E(4,7), P(4,7).

%I A010901 #35 Nov 01 2024 12:05:35
%S A010901 4,7,12,21,37,65,114,200,351,616,1081,1897,3329,5842,10252,17991,
%T A010901 31572,55405,97229,170625,299426,525456,922111,1618192,2839729,
%U A010901 4983377,8745217,15346786,26931732,47261895,82938844,145547525,255418101,448227521,786584466
%N A010901 Pisot sequences E(4,7), P(4,7).
%C A010901 Essentially the same as A005251: a(n) = A005251(n+5).
%C A010901 See A008776 for definitions of Pisot sequences.
%H A010901 Colin Barker, <a href="/A010901/b010901.txt">Table of n, a(n) for n = 0..1000</a>
%H A010901 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 A010901 Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, <a href="https://ceur-ws.org/Vol-3792/paper19.pdf">Integer sequences from k-iterated line digraphs</a>, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.
%H A010901 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 1).
%F A010901 a(n) = 2a(n-1) - 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
%t A010901 LinearRecurrence[{2, -1, 1}, {4, 7, 12}, 35] (* _Jean-François Alcover_, Oct 05 2018 *)
%o A010901 (PARI) pisotE(nmax, a1, a2) = {
%o A010901   a=vector(nmax); a[1]=a1; a[2]=a2;
%o A010901   for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]+1/2));
%o A010901   a
%o A010901 }
%o A010901 pisotE(50, 4, 7) \\ _Colin Barker_, Jul 27 2016
%Y A010901 Cf. A005251, A008776, A010925.
%K A010901 nonn
%O A010901 0,1
%A A010901 _Simon Plouffe_
%E A010901 Edited by _N. J. A. Sloane_, Jul 26 2016