This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A020750 #27 Sep 08 2022 08:44:45 %S A020750 5,9,16,28,49,85,147,254,438,755,1301,2241,3860,6648,11449,19717, %T A020750 33955,58474,100698,173411,298629,514265,885608,1525092,2626337, %U A020750 4522773,7788595,13412614,23097646,39776083,68497749,117958865,203135052,349815584,602411753 %N A020750 Pisot sequence T(5,9), a(n) = floor(a(n-1)^2/a(n-2)). %H A020750 Colin Barker, <a href="/A020750/b020750.txt">Table of n, a(n) for n = 0..1000</a> %F A020750 a(n) = 2*a(n-1) - 2*a(n-4) + a(n-5) (holds at least up to n = 40000 but is not known to hold in general). %F A020750 Note the warning in A010925 from Pab Ter (pabrlos(AT)yahoo.com), May 23 2004: [A010925] and other examples show that it is essential to reject conjectured generating functions for Pisot sequences until a proof or reference is provided. - _N. J. A. Sloane_, Jul 26 2016 %t A020750 RecurrenceTable[{a[0] == 5, a[1] == 9, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 40}] (* _Bruno Berselli_, Feb 04 2016 *) %t A020750 nxt[{a_,b_}]:={b,Floor[b^2/a]}; NestList[nxt,{5,9},40][[All,1]] (* _Harvey P. Dale_, Aug 29 2021 *) %o A020750 (Magma) Iv:=[5, 9]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..40]]; // _Bruno Berselli_, Feb 04 2016 %o A020750 (PARI) pisotT(nmax, a1, a2) = { %o A020750 a=vector(nmax); a[1]=a1; a[2]=a2; %o A020750 for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2])); %o A020750 a %o A020750 } %o A020750 pisotT(50, 5, 9) \\ _Colin Barker_, Jul 29 2016 %Y A020750 See A008776 for definitions of Pisot sequences. %K A020750 nonn %O A020750 0,1 %A A020750 _David W. Wilson_ %E A020750 Deleted unproved recurrence and program based on it. - _N. J. A. Sloane_, Feb 04 2016