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 A143684 #35 Jan 09 2025 09:52:45
%S A143684 0,0,1,1,3,7,43,603,51859,62541955,6486726488691,
%T A143684 811385112306041061811,10526466601050236861337066646958803,
%U A143684 17082036570557873538131893815781561362696563088187144467,359626974875792367278553795120318710475396935851854517275793126801351587742904492716786003
%N A143684 a(0) = a(1) = 0; thereafter a(n) = 2*a(n-1)*a(n-2) + 1.
%H A143684 Vincenzo Librandi, <a href="/A143684/b143684.txt">Table of n, a(n) for n = 0..19</a>
%H A143684 A. V. Aho and N. J. A. Sloane, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/11-4/aho-a.pdf">Some doubly exponential sequences</a>, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
%H A143684 A. V. Aho and N. J. A. Sloane, <a href="/A000058/a000058.pdf">Some doubly exponential sequences</a>, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)
%F A143684 Equals A142471/2.
%F A143684 a(n) is about 1/2*c^(phi^n), where c = 1.27817816239858832577... and phi is the golden ratio. - _Charles R Greathouse IV_, Mar 21 2012, corrected by _Vaclav Kotesovec_, May 05 2015
%t A143684 a[n_]:=a[n]=If[n<2,0, 2*a[n-1]*a[n-2]+1]; Table[a[n], {n,0,15}] (* _G. C. Greubel_, May 29 2021 *)
%o A143684 (Magma) I:=[0,0]; [n le 2 select I[n] else 2*Self(n-1)*Self(n-2)+1: n in [1..15]]; // _Vincenzo Librandi_, Nov 14 2011
%o A143684 (Sage)
%o A143684 def a(n): return 0 if (n<2) else 2*a(n-1)*a(n-2) + 1
%o A143684 [a(n) for n in (0..10)] # _G. C. Greubel_, May 29 2021
%Y A143684 Cf. A000058, A007660, A142471.
%K A143684 nonn
%O A143684 0,5
%A A143684 _N. J. A. Sloane_, based on email from Carla J. Garner-Bennett, Nov 13 2008