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

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

Offset

0,2

Links

Table of n, a(n) for n=0..73.

T. J. Osler, A proof of the continued fraction expansion of e^(1/M), Amer. Math. Monthly, 113 (No. 1, 2006), 62-66.

Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Formula

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

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

Mathematica

ContinuedFraction[Exp[1/3], 100] (* Amiram Eldar, May 20 2022 *)

Crossrefs

Cf. A016933, A058281, A092041.

Sequence in context: A294808 A294605 A060865 * A230069 A276813 A134470

Adjacent sequences: A078686 A078687 A078688 * A078690 A078691 A078692

Keyword

cofr,nonn,easy

Author

Benoit Cloitre, Dec 17 2002

Status

approved