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A010136 Continued fraction for sqrt(46). 3
6, 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12, 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12, 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12, 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12, 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12, 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12, 1, 3, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..20000

A. J. van der Poorten, An introduction to continued fractions, Unpublished.

A. J. van der Poorten, An introduction to continued fractions, Unpublished [Cached copy]

G. Xiao, Contfrac

Index entries for continued fractions for constants

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

FORMULA

a(n) = (1/396)*(-346*(n mod 12)+83*((n+1) mod 12)-49*((n+2) mod 12)+17*((n+3) mod 12)+50*((n+4) mod 12)+149*((n+5) mod 12)-115*((n+6) mod 12)-16*((n+7) mod 12]) +17*((n+8) mod 12)+83*((n+9) mod 12)-49*((n+10) mod 12)+380*((n+11) mod 12))-6*(C(2*n,n) mod 2). - Paolo P. Lava, Jul 23 2009

EXAMPLE

6.782329983125268139064556326... = 6 + 1/(1 + 1/(3 + 1/(1 + 1/(1 + ...)))). - Harry J. Smith, Jun 06 2009

MATHEMATICA

ContinuedFraction[Sqrt[46], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 16000); x=contfrac(sqrt(46)); for (n=0, 20000, write("b010136.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 06 2009

CROSSREFS

Cf. A010500 (decimal expansion). - Harry J. Smith, Jun 06 2009]

Cf. A190567. [Bruno Berselli, Nov 21 2011]

Sequence in context: A021624 A021066 A082730 * A087256 A154911 A152935

Adjacent sequences:  A010133 A010134 A010135 * A010137 A010138 A010139

KEYWORD

nonn,cofr,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 23 00:43 EDT 2019. Contains 325228 sequences. (Running on oeis4.)