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A020742 Pisot sequence T(7,9).

%I A020742 #24 Jul 06 2025 08:44:44
%S A020742 7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,
%T A020742 53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,
%U A020742 99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,131,133,135,137,139
%N A020742 Pisot sequence T(7,9).
%H A020742 Colin Barker, <a href="/A020742/b020742.txt">Table of n, a(n) for n = 0..1000</a>
%H A020742 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A020742 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A020742 a(n) = 2*n + 7.
%F A020742 a(n) = 2*a(n-1) - a(n-2).
%F A020742 From _Elmo R. Oliveira_, Oct 30 2024: (Start)
%F A020742 G.f.: (7 - 5*x)/(1 - x)^2.
%F A020742 E.g.f.: (7 + 2*x)*exp(x).
%F A020742 a(n) = A016825(n+3)/2 = A028560(n+1) - A028560(n). (End)
%t A020742 T[x_, y_, z_] := Block[{a}, a[0] = x; a[1] = y; a[n_] := a[n] = Floor[a[n - 1]^2/a[n - 2]]; Table[a[n], {n, 0, z}]]; T[7, 9, 66] (* _Michael De Vlieger_, Aug 08 2016 *)
%o A020742 (PARI) pisotT(nmax, a1, a2) = {
%o A020742   a=vector(nmax); a[1]=a1; a[2]=a2;
%o A020742   for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]));
%o A020742   a
%o A020742 }
%o A020742 pisotT(50, 7, 9) \\ _Colin Barker_, Aug 08 2016
%Y A020742 Subsequence of A005408, A020735. See A008776 for definitions of Pisot sequences.
%Y A020742 Cf. A016825, A028560.
%Y A020742 Essentially the same as A005818.
%K A020742 nonn,easy
%O A020742 0,1
%A A020742 _David W. Wilson_