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A010134 Continued fraction for sqrt(43). 3
6, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

G. Xiao, Contfrac

Index entries for continued fractions for constants

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

FORMULA

a(n) = (1/450)*(-466*(n mod 10)+29*((n+1) mod 10)+119*((n+2) mod 10)-61*((n+3) mod 10)+209*((n+4) mod 10)-151*((n+5) mod 10)+119*((n+6) mod 10)-61*((n+7) mod 10)+29*((n+8) mod 10)+524*((n+9) mod 10))-6*(C(2*n,n) mod 2). [Paolo P. Lava, Jul 23 2009]

a(n) = a(n-10) for n>10. G.f.: (6*x^10+x^9+x^8+3*x^7+x^6+5*x^5+x^4+3*x^3+x^2+x+6) / (-x^10+1). - Colin Barker, Nov 01 2013

EXAMPLE

6.557438524302000652344109997... = 6 + 1/(1 + 1/(1 + 1/(3 + 1/(1 + ...)))) [Harry J. Smith, Jun 05 2009]

MATHEMATICA

ContinuedFraction[Sqrt[43], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 16000); x=contfrac(sqrt(43)); for (n=0, 20000, write("b010134.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 05 2009

(PARI) Vec((6*x^10+x^9+x^8+3*x^7+x^6+5*x^5+x^4+3*x^3+x^2+x+6)/(-x^10+1) + O(x^100)) \\ Colin Barker, Nov 01 2013

CROSSREFS

Cf. A010497 Decimal expansion. [Harry J. Smith, Jun 05 2009]

Sequence in context: A197420 A128423 A133419 * A019713 A155824 A182429

Adjacent sequences:  A010131 A010132 A010133 * A010135 A010136 A010137

KEYWORD

nonn,easy,cofr

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified May 26 05:22 EDT 2019. Contains 323579 sequences. (Running on oeis4.)