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A078689 Continued fraction expansion of e^(1/3). 1

%I #19 May 20 2022 03:37:31

%S 1,2,1,1,8,1,1,14,1,1,20,1,1,26,1,1,32,1,1,38,1,1,44,1,1,50,1,1,56,1,

%T 1,62,1,1,68,1,1,74,1,1,80,1,1,86,1,1,92,1,1,98,1,1,104,1,1,110,1,1,

%U 116,1,1,122,1,1,128,1,1,134,1,1,140,1,1,146

%N Continued fraction expansion of e^(1/3).

%H T. J. Osler, <a href="http://www.jstor.org/stable/27641838">A proof of the continued fraction expansion of e^(1/M)</a>, Amer. Math. Monthly, 113 (No. 1, 2006), 62-66.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).

%F a(3k+1) = 6k+2, otherwise a(i) = 1.

%F G.f.: -(x^2-x+1)*(x^3-3*x^2-3*x-1) / ((x-1)^2*(x^2+x+1)^2). - _Colin Barker_, Jun 24 2013

%t ContinuedFraction[Exp[1/3], 100] (* _Amiram Eldar_, May 20 2022 *)

%Y Cf. A016933, A058281, A092041.

%K cofr,nonn,easy

%O 0,2

%A _Benoit Cloitre_, Dec 17 2002

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