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 A020737 #29 Oct 08 2022 08:33:59
%S A020737 5,9,17,33,65,129,257,513,1025,2049,4097,8193,16385,32769,65537,
%T A020737 131073,262145,524289,1048577,2097153,4194305,8388609,16777217,
%U A020737 33554433,67108865,134217729,268435457,536870913,1073741825,2147483649,4294967297,8589934593
%N A020737 Pisot sequence L(5,9).
%C A020737 An Engel expansion of 1/2 to the base 2 as defined in A181565, with the associated series expansion 1/2 = 2/5 + 2^2/(5*9) + 2^3/(5*9*17) + 2^4/(5*9*17*33) + ... . - _Peter Bala_, Oct 28 2013
%H A020737 Vincenzo Librandi, <a href="/A020737/b020737.txt">Table of n, a(n) for n = 0..238</a>
%H A020737 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A020737 a(n) = 2^(n+2) + 1.
%F A020737 a(n) = 3*a(n-1) - 2*a(n-2).
%F A020737 G.f.: -(6*x-5) / ((x-1)*(2*x-1)). - _Colin Barker_, Jun 21 2014
%F A020737 E.g.f.: exp(x)*(1 + 4*exp(x)). - _Stefano Spezia_, Oct 08 2022
%t A020737 LinearRecurrence[{3,-2},{5,9},40] (* _Harvey P. Dale_, Jun 10 2015 *)
%o A020737 (Magma) [2^(n+2)+1: n in [0..40] ]; // _Vincenzo Librandi_, Apr 28 2011
%o A020737 (PARI) a(n)=2^(n+2)+1 \\ _Charles R Greathouse IV_, Jun 05 2013
%o A020737 (PARI) Vec(-(6*x-5)/((x-1)*(2*x-1)) + O(x^100)) \\ _Colin Barker_, Jun 21 2014
%Y A020737 Subsequence of A000051. See A008776 for definitions of Pisot sequences.
%Y A020737 Cf. A083575, A083683, A083686, A083705, A168596, A181565, A195744.
%K A020737 nonn,easy
%O A020737 0,1
%A A020737 _David W. Wilson_