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A040965 Continued fraction for sqrt(997). 1
31, 1, 1, 2, 1, 4, 1, 1, 4, 1, 2, 1, 1, 62, 1, 1, 2, 1, 4, 1, 1, 4, 1, 2, 1, 1, 62, 1, 1, 2, 1, 4, 1, 1, 4, 1, 2, 1, 1, 62, 1, 1, 2, 1, 4, 1, 1, 4, 1, 2, 1, 1, 62, 1, 1, 2, 1, 4, 1, 1, 4, 1, 2, 1, 1, 62, 1, 1, 2, 1, 4, 1, 1, 4, 1, 2, 1, 1, 62, 1, 1, 2, 1, 4, 1, 1, 4, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..89.

Index entries for continued fractions for constants

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

FORMULA

a(n)=(1/507)*{-2338*(n mod 13)+41*[(n+1) mod 13]+80*[(n+2) mod 13]+2*[(n+3) mod 13]+158*[(n+4) mod 13]-76*[(n+5) mod 13]+41*[(n+6) mod 13]+158*[(n+7) mod 13]-76*[(n+8) mod 13]+80*[(n+9) mod 13]+2*[(n+10) mod 13]+41*[(n+11) mod 13]+2420*[(n+12) mod 13]}-31*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava, Jun 03 2009]

G.f.: -(x +1)*(31*x^12 -30*x^11 +31*x^10 -29*x^9 +30*x^8 -26*x^7 +27*x^6 -26*x^5 +30*x^4 -29*x^3 +31*x^2 -30*x +31)/((x -1)*(x^12 +x^11 +x^10 +x^9 +x^8 +x^7 +x^6 +x^5 +x^4 +x^3 +x^2 +x +1)). [Colin Barker, Aug 11 2012]

MAPLE

with(numtheory): Digits := 300: convert(evalf(sqrt(997)), confrac);

MATHEMATICA

ContinuedFraction[Sqrt[997], 120]  (* Harvey P. Dale, Apr 19 2011 *)

PadRight[{31}, 120, {62, 1, 1, 2, 1, 4, 1, 1, 4, 1, 2, 1, 1}] (* Harvey P. Dale, Aug 18 2016 *)

CROSSREFS

Sequence in context: A086019 A040968 A040967 * A040966 A040964 A040963

Adjacent sequences:  A040962 A040963 A040964 * A040966 A040967 A040968

KEYWORD

nonn,cofr,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 16 08:26 EST 2019. Contains 320159 sequences. (Running on oeis4.)