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A056469 Number of elements in the continued fraction for Sum_{k=0..n} 1/2^2^k. 5

%I

%S 2,3,4,6,10,18,34,66,130,258,514,1026,2050,4098,8194,16386,32770,

%T 65538,131074,262146,524290,1048578,2097154,4194306,8388610,16777218,

%U 33554434,67108866,134217730,268435458,536870914,1073741826,2147483650

%N Number of elements in the continued fraction for Sum_{k=0..n} 1/2^2^k.

%H Vincenzo Librandi, <a href="/A056469/b056469.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).

%F a(0)=2; for n > 0, a(n) = 2^(n-1) + 2 = A052548(n-1) + 2.

%F a(n) = floor(2^(n-1) + 2). - _Vincenzo Librandi_, Sep 21 2011

%F From _Colin Barker_, Mar 22 2013: (Start)

%F a(n) = 3*a(n-1) - 2*a(n-2) for n > 2.

%F G.f.: -(x^2+3*x-2) / ((x-1)*(2*x-1)). (End)

%t LinearRecurrence[{3,-2},{2,3,4},40] (* _Harvey P. Dale_, Apr 23 2015 *)

%o (Sage) [floor(gaussian_binomial(n,1,2)+3) for n in xrange(-1,32)] # _Zerinvary Lajos_, May 31 2009

%o (MAGMA) [Floor(2^(n-1)+2): n in [0..60]]; // _Vincenzo Librandi_, Sep 21 2011

%Y Cf. A007400. Apart from initial term, same as A052548. See also A089985.

%K nonn,easy

%O 0,1

%A _Benoit Cloitre_, Dec 07 2002

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Last modified October 18 00:07 EDT 2019. Contains 328135 sequences. (Running on oeis4.)