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A041794 Numerators of continued fraction convergents to sqrt(418). 2
20, 41, 184, 3721, 15068, 33857, 1369348, 2772553, 12459560, 251963753, 1020314572, 2292592897, 92724030452, 187740653801, 843686645656, 17061473566921, 69089580913340, 155240635393601, 6278714996657380 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,0,0,67714,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^11-20*x^10+41*x^9-184*x^8+3721*x^7-15068*x^6-33857*x^5-15068*x^4-3721*x^3-184*x^2-41*x-20)/(x^12-67714*x^6+1). - Vincenzo Librandi, Nov 09 2013

a(n) = 67714*a(n-6)-a(n-12). - Vincenzo Librandi, Nov 09 2013

MATHEMATICA

Numerator/@Convergents[Sqrt[418], 30]  (* Harvey P. Dale, Apr 07 2011 *)

CoefficientList[Series[-(x^11 - 20 x^10 + 41 x^9 - 184 x^8 + 3721 x^7 - 15068 x^6 - 33857 x^5 - 15068 x^4 - 3721 x^3 - 184 x^2 - 41 x - 20)/(x^12 - 67714 x^6 + 1), {x, 0, 30}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 67714, 0, 0, 0, 0, 0, -1}, {20, 41, 184, 3721, 15068, 33857, 1369348, 2772553, 12459560, 251963753, 1020314572, 2292592897}, 30] (* Vincenzo Librandi, Nov 09 2013 *)

PROG

(MAGMA) I:=[20, 41, 184, 3721, 15068, 33857, 1369348, 2772553, 12459560, 251963753, 1020314572, 2292592897]; [n le 12 select I[n] else 67714*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 09 2013

CROSSREFS

Cf. A041795.

Sequence in context: A171389 A038639 A041792 * A041796 A041798 A132762

Adjacent sequences:  A041791 A041792 A041793 * A041795 A041796 A041797

KEYWORD

nonn,cofr,frac,easy,less

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 24 12:07 EST 2014. Contains 249898 sequences.