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